According to Sky, Ms Staveley's PCP Capital Partners tabled a bid to buy Newcastle from Mr Ashley late last week following more than two months of negotiations.
Sky Sports claims Newcastle have denied the bid is worth in the region of £300m.
PCP's money is a combination of Ms Staveley's equity and that of her major investors, which include funds based in the Middle East.
And speaking as a guest on Sky Sports Monday Night Football show, former Newcastle striker Bellamy had a message for Staveley about his old club.
"Look Mike Ashley IS going to sell the club," Bellamy told MNF.
"I just look at it from the outside looking in and if there is money available and there is someone out there that's wanting to buy a football club, please go and buy Newcastle United because it's a brilliant football club, the fans.
"It just needs that lift.
"And if they can get that, and someone who is willing to invest in the squad, back the manager they'll have a good time doing it as well."