Bell, a 33-year-old veteran of 115 Tests, is now the senior member of the England side and has been on the winning side in five Ashes campaigns.
But speaking after Australia's innings and 42-run win in the fifth Test at The Oval on Sunday completed a 3-2 series win for England, Bell indicated, during a brief BBC radio interview, he would "take stock" of his future in the weeks ahead.
Strauss, once Bell's Test captain, said he was confident his former team-mate could still have an international future.
"He's at the stage of his career when he'll be thinking about what his future looks like," Strauss told BBC Radio 5 Live on Monday.
"I haven't had the opportunity to speak to him yet about it but we know the number of high quality performances we've seen from him over the years.
"If he's still got the motivation and drive to continue then he's still got a very important part to play in England cricket.
"I don't want to put words in the selectors' mouths by any means, the selectors will pick the side as they always do, but what I would say is how many great contributions Ian has made to the team not just in previous years, but in this year as well.
"For all those players who played an important part in the Ashes it's time to sit down and take a couple of days off reliving the whole series in their mind without all the pressure on their shoulders."
Meanwhile, Strauss said Alastair Cook's side, who face tough series away to Pakistan and South Africa before the end of the year, still had room for improvement.
"I'm incredibly proud of the players, support staff and families for going through some tough times," said Strauss, a former Ashes-winning skipper.
"There's lot of pressure and an Ashes series is one of those where you're either a hero or a zero," he added.
"The guys managed to win the important sessions at important times. It's nice to be sitting in the background taking some sort of reflected glory from it but it was all down to Alastair Cook and his guys.
"But we're very conscious this is a young, developing side and there's a lot of hard work to do.
"The final Test showed to everyone that we're not the finished article by any means...but it's nice to be Ashes winners."
jdg
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