Several other media, including Bild newspaper and Kicker magazine, citing unnamed sources, also said a deal could be finalised in the coming days.
Two goals from Marco Reus spurred Borussia Dortmund to lift the German Super Cup with a 4-2 win over Champions League and Bundesliga holders Bayern Munich on Saturday.
The gaze of the sporting world will fall on Germany this weekend as the Bundlesliga becomes the first major soccer league to emerge from the shutdown caused by the coronavirus pandemic. All 18 clubs will crank back into action in what could act as a catalyst for other leagues to follow suit.
Dortmund's Ciro Immobile hadn't scored since joining the club this season. But while he was getting restless, the striker was asked by coach Juergen Klopp to be patient and persistent.
Borussia Dortmund edged past Freiburg 1-0 on Sunday courtesy of captain Sebastian Kehl's first goal in almost two years to go four points clear in second place in the Bundesliga.
Robin van Persie's hat-trick lifted the gloom surrounding Manchester United and manager David Moyes as the English side beat Olympiakos Piraeus 3-0 to overturn a 2-0 first-leg deficit and reach the Champions League quarter-finals on Wednesday.
Depleted Borussia Dortmund shrugged off the absence of more than half a dozen starting players to ease into the German Cup quarter-finals with a comfortable 2-0 win at third-tier Saarbruecken on Tuesday.
Arsenal's Jack Wilshere and Kieran Gibbs are doubtful for the Champions League Group F trip to last season's runners-up Borussia Dortmund with coach Arsene Wenger eager to make amends for last month's loss to the Germans.
Karim Benzema came off the bench to score 13 minutes from time and ruin any chance of a dream result for resilient Ludogorets as holders Real Madrid carved out a patchy 2-1 win in Wednesday's Champions League Group B match.