Sunderland are hoping to retain the services of defenders Alan Hutton and John Mensah.
Tottenham full-back Hutton has enjoyed an impressive spell on Wearside since joining on loan in January, while Mensah has shown his quality despite his season-long move from Lyon being repeatedly interrupted by injury.
Asked about Hutton, chairman Naill Quinn said: "We have been happy with Alan. I sat down with him on Friday morning and was delighted to hear his desire to come permanently to Sunderland. I now have to contact (Spurs' executive chairman) Daniel Levy to see if this is possible."
On the subject of Mensah, chief executive Steve Walton - who was participating with Quinn in a webchat with fans on the club's official website - replied: "John's a really tough one. He wants to stay, we want him to stay and I'm hoping to visit Lyon shortly to try and strike a deal for another year.
"But the original proposal cannot be accepted. Watch this space."
Walton, who also confirmed the club is working on a deal to bring Paraguayan midfielder Christian Riveros to Wearside, insisted there will be no high-profile departures from the Stadium of Light this summer.
He said: "There is no way we will sell any of our top players, except for crazy money. It's about getting better every year, not going backwards."
Asked specifically if he was concerned about the Premier League's leading clubs expressing an interest in top scorer Darren Bent, Quinn replied: "If so, it's great that they are because it means we are in a very good place with a very good player. We see Darren being phenomenal for this club for a long time to come."
Quinn also admitted he is looking forward to the return of the derby clashes with Newcastle following the Magpies' promotion from the Coca-Cola Championship at the first attempt.
He added: "Can't wait, it's been sorely missed this year. Never mind commercially, our football club has missed out emotionally without the derby. The build-up, the aftermath, the passion, bring it on."
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