Trescothick opted out of the Champions Trophy in India next month because he is still struggling to shake off a gastrointestinal infection and a stress-related illness that forced him off the India tour earlier this year.
His decision has raised doubts about his participation in the fourth one-day international against Pakistan at Trent Bridge Friday and the final game at Edgbaston on Sunday.
But Trescothick's place in the first Ashes Test against Australia in November could also be under threat.
"Australia is going to be a big Test for all of us and it will be a big Test for Tres as well," Strauss said.
"He's still focused on playing for England despite the fact he's not going to India. He remains committed to playing for England as long as he can.
"He hasn't got to the stage he has in his career without being able to overcome Tests. I don't see any reason why he won't do it again.
"It's so hard to put a value on what he means to the team. He offers
GOOD ATMOSPHERE
"He's always helping out people when he can, he's always trying to provide a good atmosphere in the dressing room and he's an example for us to follow.
"Let's just hope his absence is only for four or five games or whatever it is in India."
"There's no reason why he shouldn't go on and play a full part in the Ashes and beyond."
However, it may be a gamble for the England selectors to pick such a vulnerable player against the world champions.
Particularly a player who has averaged just 19 in Tests during the Sri Lanka-Pakistan series and has scored only one hundred.
But England are set to throw their support behind Trescothick, who has never been dropped since making his debut against the West Indies in 2000.
"There's not a huge amount that his team mates can do to help him. He's the only one that can tell you how much it affects him while he's at home, or whether it's just away from home.
"We all want to see him playing for England as soon as possible and for as long as possible."
