The 34-year-old practised for an hour on Thursday evening at the Rod Laver Arena and his fitness was improving "little by little, step by step", sources close to Nadal told Reuters.
Novak Djokovic is finally set to return to action next week after six months out with an elbow injury and will then decide whether to take part in the Jan 15-28 Australian Open.
Holder and top seed Novak Djokovic suffered an almighty scare against South African giant Kevin Anderson before bad light halted play with the score tied at two sets all in their fourth round match at Wimbledon on Monday.
Top seed Roger Federer was finally forced to work hard for a win at the Swiss Indoors tournament as he fought back to beat Adrian Mannarino 4-6, 6-1, 6-3 in his quarter-final on Friday.
The 32-year-old has not played singles since losing in the first round of the Australian Open in January to Spain's Roberto Bautista Agut, after which he underwent hip resurfacing surgery in a bid to salvage his career.
Medvedev suffered a jarring early exit from the Canadian Masters last week but overcame some initial problems in a tricky tie against Shapovalov to edge both sets and book a meeting with American Fritz.
American Frances Tiafoe celebrated his 21st birthday by stunning Bulgaria's Grigor Dimitrov 7-5, 7-6(6), 6-7(1), 7-5 in the fourth round of the Australian Open on Sunday.
Bhambri, ranked 116 in the world, had reached the second round when the ATP 250 event was played in Chennai in January 2017.
The winners of the Serbia-Germany tie will join Spain, Russia and Italy in the semi-finals.
Bautista Agut played in Spain's victories over Russia and Croatia but left the team and returned to Castellon after the health of his father Joaquin deteriorated.
A round-up of all tennis action on Friday.
World number one Ash Barty delighted the Memorial Drive crowd by breezing through to the Adelaide International semi-finals with a comfortable 6-3, 6-4 victory over Sofia Kenin on Friday.
'I have so much to look forward to in 2021, including the Olympics'
We spotted some celebs from the world of Hollywood, cricket and comedy enjoying some tennis action and here we give a glimpse of them...
Frances Tiafoe is hopeful to build on his own stature in the game as he prepares for an Australian Open quarter-final clash with Rafael Nadal on Tuesday.
We bring you best images from week one of the 2019 Australian Open Championships at Melbourne Park
Top seed Novak Djokovic made quick work of Tennys Sandgren at the Western and Southern Open on Tuesday, never dropping serve en route to a 6-2, 6-4 win over the American, while big-serving Milos Raonic enjoyed a straight sets win over Andy Murray.
World number one Novak Djokovic is on verge to become the first man to win US$100 million in prize money as he aims to book his place in the quarter-finals of the French Open for the 10th time.
Roger Federer reached the Rogers Cup semi-finals on Friday after coming to the net early and often in a straight sets victory over Roberto Bautista Agut on a windy day in Montreal.
The 20-year-old became the youngest semi-finalist at Melbourne Park since American Andy Roddick, also 20, at the 2003 tournament.
The World number 14 subdued the young Russian 6-3, 6-4 to capture his fifth ATP singles title.
Yuki Bhambri and his New Zealand partner Michael Venus registered a straight sets victory on their Grand Slam debut, but Divij Sharan's Australian Open campaign ended in the first round, in Melbourne, on Wednesday.
Former world number one Novak Djokovic's preparation for next month's Australian Open suffered a blow after he pulled out of the season-opening exhibition event in Abu Dhabi on Friday due to pain in his right elbow.
Andy Murray has lost the world number two spot to Roger Federer in the latest ATP rankings released on Monday, after his defeat to Novak Djokovic in the Madrid Masters final.
Clearly Nikoloz Basilashvili had come to face Rafael Nadal with a plan but, like Mike Tyson said, everybody has a plan until they're punched in the face.
Richard Gasquet won a 13th career singles title by beating fellow Frenchman Paul-Henri Mathieu 7-5 6-4 in the Open Sud de France final in Montpellier on Sunday.
The comment came shortly after Murray revealed that the 2019 Australian Open could be his last tournament.
Britain's Andy Murray enjoyed a routine win over Argentina's Juan Monaco to ease into the third round of the tennis tournament at the Rio Games on Tuesday, while Spain's world number nine David Ferrer was knocked out.
World number two Novak Djokovic expects Stanislas Wawrinka and Andy Murray to lift their game at the French Open despite failing to make an impact so far in the clay court season.
Rediff.com encapsulates all the sporting action from the past week in this eye-catching photo feature.
It was Roger Federer's fastest defeat since losing to Franco Squillari in 54 minutes in Sydney in 2003.
A tenacious Roberto Bautista Agut battled back to beat world number one Novak Djokovic 1-6, 7-5, 6-3 and advance to the quarter-finals of the Miami Open on Tuesday as the Spaniard claimed his second win over the Serb this year.
Raducanu stormed into the third round of the Cincinnati Open
Simona Halep ended Beatriz Haddad Maia's dream run in Toronto
Australian Nick Kyrgios produced another extraordinary performance to demolish compatriot Alex de Minaur 6-2, 6-3 at the Canadian Masters on Thursday, a day after stunning world number one Daniil Medvedev.
Daniil Medvedev fired Russia into the final of the ATP Cup on Saturday with a tense 3-6, 6-3, 7-5 win over an injury-hampered Alexander Zverev after the German destroyed a racket in frustration over a lost service break.
Stefanos Tsitsipas' YouTube channel is experiencing a surge in subscribers after he reached the Australian Open semi-finals and the Greek youngster will hope to add to his highlight reel when he faces world number two Rafael Nadal on Thursday.
Off-court distractions and a neck injury could not prevent Novak Djokovic from extending his winning run this year to 23 matches and the Serbian could not be in more intimidating form ahead of the US Open.
The wild card team of India's Yuki Bhambri and Michael Venus of New Zealand created a big upset at the Australian Open, shocking tenth seeds Jean-Julien Rojer and Horia Tecau in Melbourne on Friday. They needed just 64 minutes to get the better of the experienced Dutch-Romanian pair 6-4, 6-4 in a second round match.
Images from Day 7 of the 2021 Wimbledon at the All England Lawn Tennis and Croquet Club, in London, on Monday.
