Riise's return to Roma's first-team has painted a brighter picture for the former Liverpool defender, but he told Newcastle he was not interested even when he was out of the side.
His agent has informed the Newcastle boss his client will be staying with the Serie A outfit until the end of the season.
Kinnear (talking to the Daily Mirror): "If we can get like-for-like then I'll lose one.
"We've gone down that road already but I got a knock-back.
"John Arne Riise changed his mind, but if we'd got him in then I could have done something with Enrique.
"Riise's got back in the team at Roma and his agent has told us that he's happy to stay until the end of the season. I want them now, really."