The Latics' chief urged the Blues to make a decision over the 21-year-old as it effects their own dealings, revealing they'll sell the player for a up-front sum close to £9 million
The Blues have been linked with the attacker throughout the summer, despite already signing the likes of Oscar, Eden Hazard and Marko Marin, and have reportedly had two offers turned down by the Latics.
Whelan admitted that offers of sorts have been made but insisted that he will only accept a flat out sum, also revealing his valuation does not match his manager's.
"Roberto [Martinez] actually thinks I've put too low of a figure on him, I've told Chelsea what we want," he told Sky Sports.
"They've offered certain things but one of them was on appearances and I'm not too keen on appearances because all kinds of things can happen at a football cub like Chelsea. You can play one game out of six in the first team there is so much competition. You could get injured.
"I've asked them for a fee, if they pay the fee we release him, if they don't then we keep him."
Whelan then revealed that his asking price was "not as much as" £10 million, and that £9m was "not far off".
The chairman then expressed his annoyance at the Blues' hesitation over the move, suggesting that his own club have been left in limbo as they wait to make a decision on whether they need to dip back into the transfer market, adding to the likes of Mauro Boselli, Ramis and most recently Ryo Miyaichi.
"We could do [more business], it depends on [Chelsea]." He added. "[They] have to make their mind up, and at present they're messing about a little bit, which is unusual for Chelsea because usually they're up front and if they want somebody they'll go and make a bid and get him.
"With Victor they've sort of moved in and made offers and payments later. It's unusual with Chelsea because usually they're a very straight forward club.
"If they come with the fee we'll sell him, if they don't we'll keep him."
"Roberto is the man who decides what players he want and what positions he's looking for. I try and back him, if we can't afford it I tell him the truth and he respects the truth at all times.
"If we sell young Victor we probably will go back in the market. I'd like to keep Victor, I think he'll benefit enormously from playing another season or another two or three seasons under Roberto."
Martinez's men kick-off their new season against Chelsea on Sunday, with it still not yet clear which side the 21-year-old will turn out for.