David Moyes has no intention of selling Lamine Koné if he can possibly help it and believes it would be impossible to sign as good a central defensive replacement for the £21m Everton are prepared to pay.

“Koné will stay,” said Sunderland’s manager before suggesting that, although he had vetoed Everton’s bid, it had not been turned down outright by his board.

“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.”

Koné was ordered by Moyes to stay away from the club after the Ivory Coast international ruled himself out of the home defeat against Middlesbrough on Sunday with a self-diagnosed back complaint but he is due to return to the training ground on Wednesday for assessment by the club’s medical staff.

That department has been busy of late with a list of injuries to key players extended by the suspected broken elbow sustained by Vito Mannone, Moyes’s first‑choice goalkeeper, in training. Mannone was taken to hospital on Tuesday for X-rays.

Moyes, who on Wednesday will hope for his first win since succeeding Sam Allardyce, in the EFL Cup at home against Shrewsbury Town, said he had been realistic rather than defeatist to suggest Sunderland are virtually condemned to yet another relegation fight in the wake of the Middlesbrough defeat. The club’s debt currently forces them to shop in the bargain basement department.

“The club has just avoided relegation in each of the last four years or so,” the former Shrewsbury defender said. “I don’t want that to happen again, I want to get us up the league. But it can’t happen overnight. I can’t change it overnight.”

More immediately he hopes to avoid a slip‑up against Shrewsbury, a team he will treat warily after suffering FA Cup defeat by the Shropshire side as Everton manager in 2003. “It was probably one of the worst days I had as Everton manager and I had a few,” said a man working with a strictly limited budget under which, so far, he has added mainly squad players to an under-strength group that has lost Younès Kaboul to Watford.

“I’ve got full faith in the owner [Ellis Short],” said Moyes, who is hoping to conclude deals with Rubin Kazan for the midfielder Yann M’Vila and Barnsley for the defender Alfie Mawson and desperately needs a new striker to complement Jermain Defoe. “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.”

He illustrated his point by explaining Sunderland could not compete with Watford for Everton’s James McCarthy. “I don’t know if we’d have that kind of cash to spend on just one player,” he said. “I hope it won’t be the case in a couple of years’ time.”