The midfielder, 30, arrived from Leeds on Saturday morning on a loan deal until the end of the season and duly made his debut off the bench in the 2-2 draw at Barnsley.
Town boss Mick McCarthy has already admitted the Republic of Ireland international, whose current contract at Elland Road expires in the summer, has the chance to land a long-term deal at Portman Road.
And Green aims to do just that by helping Ipswich secure a top-six finish.
"The gaffer is renowned for getting clubs up, so it was a big thing for me that he wanted me here," Green told the club's official website.
"I know I'm not going to jump straight into the team here because the players have been doing well. I've got to bide my time and take my chance when it comes.
"I'm looking forward to my time here and hopefully I can help the club reach the play-offs."
He added: "I think it is finished for me at Leeds. It's a shame because I loved it there but that's football.
"The manager has said that there may be something here at the end of the season if I play well so it's a possibility. We will have to see how things work out but it would be great if something could be done."