The Republic of Ireland international was signed by Steve Bruce in 2011 but did not get the chance to play on a regular basis until Martin O'Neill came to the Stadium of Light.
McClean appears to fallen out of favour under new boss Paolo Di Canio though and Whelan says they are closing on a deal for him, whilst admitting players would be allowed to leave if a big club expressed an interest in signing them.
"We have got to have discussions with his agent but we have agreed a fee with Sunderland and the lad is here talking to us now," Whelan told Sky Sports News.
"I am sure there is interest in two or three of our players but we want to keep them all. I have told the lads that and the boss is with me and we want to keep everything we have got.
"But I have promised the players that if a big club comes in for them, I will not stand in their way and if we get the right deal, we will allow them to go.
"At present we are managing to hold onto everybody and we are just in the process of signing another new player (McClean)."
Whelan also praised manager Owen Coyle for the progress he has made since taking over form Roberto Martinez at the DW Stadium.
Coyle has been busy in the transfer market as he attempts to bolster his squad, something Whelan feels will be crucial as they prepare for extra games in the Championship as well as competing in the Europa League.
"We were sorry to lose Roberto but we have got to get on with it. We interviewed half a dozen good lads but we just thought Owen was the right man," added Whelan.
"He has put a new feeling into the club and we have 11 new players in.
"We have 56 games this season so Owen is doing the right thing and I have encouraged him to get players in.
"We will then be ready for all the competitions."