The Dutch giants were considered the strong favourites to sign the forward before he becomes a free agent in the summer.
But the Premier League trio are understood to have been monitoring the situation closely, and are ready to pounce at the end of the season should Ajax fail to reach an agreement.
Muric has rejected the chance to stay in Croatia, and has refused to sign a new deal with Dinamo Zagreb.
He will walk away when his contract expires at the end of the season, although it is still unclear as to where he will end up.
The Croatia Under-17 star was reported to have given his word to Ajax, but the club have admitted a deal is yet to be agreed.
Technical director Marc Overmars said: “Muric is wanted by many clubs – everybody wants him.
“He really is a great talent and will be a free agent in the summer. But he is not yet ours.”