O'Brien has been training with Motherwell for the last few weeks after being told he is well down the pecking order at Parkhead.
Well boss Mark McGhee has been suitably impressed by the Irishman and is now waiting to see if Celtic will accept his offer for the player.
"I've spoken to Celtic about Jim O'Brien and I await their answer to my proposal," McGhee told the club's official website.
"I think, if he signs, we're going to have to work very hard with Jim and he's going to have to work very hard with us. In saying that, he has got great energy; he's as fit as anybody which allows him to run all day. Over and above that, he's got pace and has a trick or two in his locker.
"It will be our job, if he signs, to get it all under control and get the very best from him. If we can do that then I think we've got the potential to acquire a very decent player."
Lappin spent a spell on loan at Fir Park and the former Scotland Under 21 international does not figure in Glenn Roeder's plans at Carrow Road.
McGhee had expressed his fear that Motherwell would not be able to afford Lappin, but he is not giving up hope of doing a deal for the former St Mirren man.
"It's not impossible!" added McGhee. "However, I think you've got to be clear though that, when Norwich say that he can go permanently, they are not prepared to move him on for nothing.
"You would then have a fee over and above Simon's wages, which could well be above our budget, so that may prove to be difficult."