Wright-Phillips, 29, made just two Premier League starts for City last season and looks certain to leave Eastlands three years after he rejoined the club from Chelsea.
Bolton have emerged as favourites to sign the England international in recent weeks, with Trotters defender Zat Knight recently claiming that Wright-Phillips wanted to join him at the Reebok Stadium.
"Shaun's a very good friend of mine and, speaking to him, he'd love to come to Bolton," Knight said. "He's at that age where he needs to be playing week in, week out. He hasn't played regularly for the last two seasons.
"If he had to take a pay cut then I think he would do, because he could progress at Wanderers and then something else could happen."
But Wigan could be ready to step in and hijack any move for the wide man, with Whelan claiming that Martinez is a fan of Wright-Phllips.
"It's true that we are interested in Shaun Wright-Phillips and I am sure that he would love it at Wigan because in Roberto Martinez we have a great manager," Whelan said.
"But am I confident we can get him? Well confidence is something that you can't have at this time of the year.
"We would certainly like him to come to Wigan but we don't know what he wants in terms of wages. There is a long way to go, but Roberto does fancy bringing him to Wigan."
It's believed Wright-Phillips could be priced at as little as £3 million as Roberto Mancini is keen for him to move on; the former Chelsea man had seemed destined to leave in the January transfer window, but an injury to Adam Johnson meant he was retained as extra cover.