McClaren said: "Steve played against Chelsea a couple of weeks ago and ultimately he wants to play next week.
"He knows how important these games are and he knows he's an important member of the team.
"Players have to have a passion to play for their country. And nobody epitomises that more than Stevie G.
"He's always turned up and always wants to play, even for the last game against Germany. That's the type of character we need. Believe me, he is strong enough to indicate to me that he wants to play in the next two games for England.
"The last time we decided there was too much risk involved for a friendly. There is a certain flexibility involved in those games. But now we're into the qualifiers. These are big, important games and the whole country wants us to be in Switzerland and Austria next summer.
"We will continue to liaise with Liverpool and the medical team but, ultimately, the decision will be made by ourselves and the player."