“We’re getting the gloves out in the next week or two and if there’s a chance to get him we’re going to fight hard to do that,” Costanzo told The World Game.
“Right now I’m putting something together to try to make it interesting for him, as other clubs are doing at the same time as well, and I would say this will probably play itself out in the next week or two.
“If he decides he wants to keep playing in the A-League somewhere, then we would back off. If not, then I’d say a little bidding frenzy would develop, wouldn’t it?”
Thompson, 37, played his last game for Victory in their AFC Champions League round of 16 second leg away game against Korean team Jeonbuk Motors on Tuesday night, with the Victory beaten 2-1 and eliminated 3-2 on aggregate.
The former Australia striker, whose A-League contract runs out on 31 May, has indicated he wants to play on rather than retire.
There have been suggestions one or two of the weaker A-League clubs, including Central Coast Mariners and Newcastle Jets, could make him an offer for next season, but there is no hard evidence that either have gone down that track at this stage.
But the interest from Whittlesea is very definite. The club is second on the table midway through the NPL 2 season and the team that finishes first past the post is automatically promoted to the top tier of the NPL next season.
The second-placed team also gets a chance to go up via a two-game playoff series.
“The facts are that, yes, we as a club are interested in Archie, and, yes, we do have the contacts that are also the major sponsors of Melbourne Victory, in La Ionica and Oliana,” Costanzo said. “They are also sponsors of our club.
“What we’re saying is if he’s going to play at a lower level we’d love to get him to play at our club.
“I do know my co-director, Sam Cuteri, had a coffee with Archie before he played those final two Asian Champions League games. Sam is from La Ionica and he would talk to Archie on a regular basis, at games and functions.
“We respect Archie’s situation at the moment, in that he’s just finished the Asian Champions League and also I do believe he may have a small offer from either Central Coast Mariners or Newcastle Jets.
“It all depends on where he wants to go from here, but we’re looking at something after he’s finished playing football as well. We’re looking at a coaching or mentor role and he would probably have something like that through Victory as well.
“We’ve got a close working relationship with Victory. Their youth team are now playing from our home ground at Epping Stadium.
“We’re very serious about this. All of the NPL clubs are trying to bolster their playing ranks at this time of the season and we’re pushing for promotion, so what we do right now is very important.”
There have been suggestions that the Victory could employ Thompson in a club ambassador role, but it remains to be seen whether, if that was on offer, he would want to move out of Melbourne to keep playing in the A-League.
Playing for an NPL 2 club with ambition could be a handy alternative that could link up with a possible new career direction at Victory.
Costanzo said the club would need the help of sponsors to make an offer attractive enough for Thompson to consider.
“Absolutely, you’d have to look at some kind of package,” he said.
“But it depends on whether discussions are going to become a bit more serious. I’ll leave that to my co-director to establish.
“I’ve heard rumours about possibly Bulleen Lions, South Melbourne, a few clubs here and there being interested in him. He’s 37, but the way he has finished off in the A-League his body is still up to it.
“And if he’s still up to playing A-League, then he’s more than up to playing in the NPL or NPL 2. He would be a superstar at that level, even next year at the age of 38.”