Lamine Kone "will stay" at Sunderland according to manager David Moyes, despite rumours of an impending exit.
Premier League rivals Everton have put in a bid for the 27-year-old, but Moyes wants to keep hold of the central defender.
While he confirmed the bid has not been turned down by the Sunderland board, Moyes insists he wants to keep Kone at the Stadium of Light.
"Kone will stay," he said. "The offer's been rejected by me, yes. I've had that offer for a while now and I could have invested the money two weeks ago but doing that is very difficult.
"Given the prices, it would be very difficult to replace Lamine. Unless we could get a suitable replacement, I would never do the deal."
Moyes also conceded he is not used to being at a club with such a restricted transfer budget, but is hoping to bring in a few players before the window closes next week.
"I've got full faith in the owner [Ellis Short]," he said. "But there's no doubt that our budget is not at the level of many other clubs you see buying players at the moment.
"I'm confident we'll get a few in before 1 September but the quality of the players that Sunderland can get at the moment is probably not what I've had in the Premier League. Not even close.
"You look at our competitors and what they're spending and we're having to deal differently."
Sunderland are without a win from their opening two Premier League fixtures, suffering losses to Middlesbrough and Manchester City.