The Chelsea midfielder picked up his 94th England cap after coming on as a substitute for the second half in the 2-1 friendly victory over Brazil at Wembley.
And the 34-year-old, who has been linked with a move to the United States this summer, once again played a starring role for his country with a brilliant winning goal in the 60th minute.
Hodgson said: "Frank was excellent. I think he can reach 100 caps.
"I hope we'll keep Frank in England. It's not for me to discuss his future with his current club, that's for him and his club. I know he'll have a lot of offers if Chelsea do decide they're prepared to let him go.
"I'm rather hoping we'll still see him, if not in England then Europe which will make my task easier. If he goes further afield and follows David (Beckham to the MLS), it complicates matters but it doesn't mean your career is over with England.
"But the further afield you go, the more problematic it gets for the media and the England manager to follow you."