The Spaniard was linked with moves to Liverpool and Aston Villa but according to Whelan will stick with the Latics, having been given his chairman's word he will be backed in the transfer market.
Whelan told ESPN: "Roberto is staying with us and I've agreed to his request to up our spending on youth development and training facilities."
He added: "That's going to be pretty costly as I have agreed to a full-sized indoor pitch - and that will cost £1.5million.
"Roberto's very keen on that aspect of the club. I have also agreed with him to bring in three or four new players."
Martinez, linked to Villa despite rejecting an offer to manage the midlands club at the start of last season, met Liverpool owners Fenway Sports Group in America last week to discuss the current vacancy at Anfield.
However, Whelan told ESPN: "They set down their rules on how they saw the role and the way they wanted the team run and that was not the way Roberto would do it.
"Roberto has his own way of doing things but they are American owners who have their own ideas of how it should be done. They are entitled to want to do it their way and Liverpool are a big club so I can see why Brendan Rodgers has opted to go there - and good luck to him he's a fine coach."
Rodgers was reported to be on the brink of leaving Swansea for Anfield.
"But I don't think Swansea are going to be too pleased," Whelan said. "They lost Roberto to us and they were none too happy about that and now they have lost Brendan so I imagine they will be even more unhappy right now."