England head coach Fabio Capello watched Downing - and Ashley Young - produce outstanding performances in the 4-1 win over Blackburn on Saturday.
Houllier believes Downing has overcome any reservations he may have had over the broken foot which sidelined for eight months, and said: "I think the injury was maybe in the back of Stewart's mind at the beginning of the season. But now he looks like he's doing well and enjoying it. Stewart is outstanding. He has improved a lot."
He added: "Stewart is more confident, he can pass, he can score, his goal against Blackburn was fantastic.
"He can make runs sometimes to cover, sometimes to fill in, and his technique is good, his awareness is good.
"Stewart can play on either side, right or left. He's one of the rare players who can use his right or left foot,
"I hope he is in the next England squad, for us and for Stewart's sake, because I like it when our players go and play for their country."
Source: PA
Source: PA