Whelan confirmed Swansea had made a formal approach Wigan's chief executive Jonathan Jackson on Thursday morning.
"We don't want to lose the lad, he's a good lad," said Whelan. "But you can't stand in their way if they want to progress."
The Swans agreed a £7m compensation deal with Liverpool to release Rodgers from his contract, and for first-team coach Colin Pascoe, match analyst Chris Davies and conditioning expert Glen Driscoll.
Jenkins as vowed to move quickly to find a successor to Rodgers.
Managers in Spain and the Netherlands have come under consideration, while Brighton's Gus Poyet, Blackpool's Ian Holloway, Birmingham's Chris Hughton and former Denmark international Michael Laudrup have joined Jones in the running for the vacancy.
Jones spent a successful spell with Swansea from 2007 to 2009 as an assistant manager under Roberto Martinez.
The former striker was a popular figure around the Liberty Stadium and was understood to have turned down the chance to succeed Martinez before opting to follow the Spaniard to Wigan.
During his time in south Wales, Jones won the League One title in 2008 and flirted with the play-offs the following season in the Championship.
Martinez was linked heavily with the Liverpool before they opted for Rodgers. He also held talks with Aston Villa but has now
pledged his future to Wigan,
according to Whelan.
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