The Iron boss, who also quashed talk of a bid to bring defender Cliff Byrne back to the club, believes Clarke, who played under Laws at Sheffield Wednesday and spent three months on loan at Scunthorpe last season, wants to stay in Sky Bet League One.
"It would be nice (to sign Clarke)," Laws told the club's official website. "He's a great player and will score goals in whatever division he'll play in, but he wants to play in at least League One.
"That doesn't mean that we can't go in, and I know the chairman will back us up, not just financially but in signing the right kind of player.
"Realistically we wouldn't have any hope of signing Leon, not at this stage.
"He's available because of Coventry's current financial situation, but he's also on a very high wage as well which we wouldn't be prepared to pay. He'll have a lot of clubs chasing after him that will be prepared to pay."
On the possible return of Byrne, Laws added: "We've sort of moved on from that in a way, that's the way football is I'm afraid, so as far as we're concerned that deal is gone unless something drastically changes."