The midfielder, 30, signed for Town from Leeds United on Saturday morning on a loan deal until the end of the season, duly making his debut off the bench in the 2-2 draw at Barnsley.
And McCarthy admits positive displays between now and May could see Green land a long-term deal at the Suffolk club, with the Republic of Ireland international's current contract soon to expire at Elland Road.
"He's a good signing for us and I thought he was excellent when he went on against Barnsley," McCarthy told the club's official website.
"He was unfortunate not to get the winner, though it was great defending from them to get the block in.
"Paul's a quality player. He's got a goal in him and he's an experienced central midfield player and we've not got a lot of them.
"He's a proper character as well, just like Frazer Richardson, and that's why I like him.
"He's out of contract in the summer and he will be looking for a deal somewhere. If he does well with us, then why not let it be here?"