Carragher could be given the chance to prove his worth at centre-back, having already filled both fullback positions this season, if Stephane Henchoz fails to recover from a groin injury in time for Saturday's trip to Birmingham.
Houllier said: "Stephane is improving every day and we will assess him at the end of the week. But Jamie filled in for him at the weekend and he fully deserved the man-of-the-match award.
"He rarely gets the recognition, as much as he deserves it. But we know his qualities here. He is useful in many different positions and that's why I think England should take him to Euro 2004.
"I don't want to put pressure on Sven Goran Eriksson because I know how difficult his job is but Carra can play left-back, right-back, centre-half and centre-midfield - and you need players in the squad that are versatile.
"His skill level has also really improved. He is more composed on the ball and technically he can do things now which I wasn't used to seeing.
"This is because he trains well and always gives 100 per cent every day. He knows he is appreciated here. After all, we gave him a new contract when his leg was still in plaster."