It was reported on Monday that both clubs had made offers in the region of £2.5million for the 25-year-old Scotland midfielder.
Holloway has previously said Adam would only leave if one of the Barclays Premier League's biggest clubs come calling - with a sizeable offer - and he insists that position has not changed.
When asked if it was correct the Seasiders had snubbed offers for Adams from Blues and Villa, Holloway said: "It's true. I spoke to Charlie this morning and he knows where I am coming from, and I know where he is coming from.
"The chairman has had a couple of calls and he has told those clubs exactly where we are.
"We have got no reason to sell anyone. We are a well-run club and we want to add in this window, not lose anyone."