The Northern Ireland legend is available for free after his contract with the Glasgow giants expired.
And the 32-year-old striker now appears certain to try and resurrect his stuttering career in England, or further afield, in the weeks ahead.
His agent Stephen Hughes said: "David would love to play for Rangers, but I think he feels that chapter of his career is over."
The lifelong Rangers supporter's departure could be the first of many at Ibrox during the close season.
The get-out clauses top Light Blues players had inserted in their deals when they agreed to take pay cuts to keep the club afloat back in March can now be activated.
Stars like Steven Davis, Kyle Lafferty, Allan McGregor and Steven Naismith can all leave for a fraction of their actual value if a big enough bid is received.
Prospective owner Charles Green is attempting to take the club out of administration via a CVA – but uncertainty still surrounds the future of the 54-times Scottish champions.
Healy's agent revealed his client, who turned down a move away from Rangers in January, had lost "a fortune" by agreeing to the cost-cutting measures.
However, Hughes stressed the player, who became his country's most-capped outfield player when he came on against Holland to make his 92nd appearance on Saturday, just wants to play football.
Healy has been interesting Fleetwood Town – after the Football League newcomers sold top scorer Jamie Vardy to Leicester City for £1million.
Elsewhere, Crawley Town, and several top-flight Scottish clubs, are also keen to secure the services of the prolific frontman.
Of the Fleetwood interest, Hughes said: "They wanted to know his situation, to find out what is happening with him. But we aren't 100% sure what's happening. To be honest, we have got an open book. I am talking about clubs higher up. David just wants to get a contract and play.
"He would love to play for Rangers. I don't know how it's going to work out. I think he thinks that chapter of his career is over.
"David feels he has got goals in him. He got into the Rangers team in January and scored four goals in seven games. I don't understand how he didn't feature more.
"He came on for Northern Ireland at the weekend. They were heavily beaten by Holland, but he still managed to get a shot on target in the 10 minutes he was on the park.
"I don't know how the situation is going to resolve itself at Rangers. The club has debts and that have this tax case hanging over them."
The veteran striker's agent added: "David had a fantastic offer from a club in January. He could have gone and played in the Champions League. But he stayed loyal to Rangers. It has cost him a fortune.
"He wants to play and we have got a few clubs that are interested. He also wants to settle for the sake of his family.
"People don't see that side of a footballer's life. He has two young kids and they have had to put up with a lot of upheaval, moving schools all the time. It is hard on them.
"There are other Scottish clubs interested in David, but I think he feels he has played up in Scotland and would like to look to other countries and abroad."
