Stoke want to resolve captain Ryan Shawcross’ future “sooner rather than later” and agree a permanent deal for fellow defender Bruno Martins Indi.
Shawcross is out of contract at the end of next season, while Martins Indi spent last term on loan from FC Porto.
“He’s been a great player for the club,” chief executive Tony Scholes said of 29-year-old Shawcross.
On Martins Indi, 25, he added: “It’s not just us, not just Bruno and his agent, there’s Porto as well.”
Next season will be English centre-back Shawcross’ 11th at Stoke, having made 380 appearances since signing, initially on loan, from Manchester United in August 2007.
Scholes told BBC Radio Stoke the English centre-back has been “a huge part of what we’ve achieved over the years and we hope that remains the case for many years to come”.
“When you’ve got important players, you want to do something sooner rather than later,” he said.
Netherlands international Martins Indi did not miss a league game for Stoke in 2016-17 after making his debut in the 4-0 home defeat by Tottenham in early September.
“Everything has to fall into place before a deal gets done,” said Scholes.
Stoke were 13th in the Premier League last season, their lowest finish since manager Mark Hughes took charge, after three successive ninth-place finishes.
‘No conversations’ about Rooney coming to Stoke
Scholes has also confirmed Stoke’s lack of interest in signing 31-year-old Manchester United and England forward Wayne Rooney.
The Potters were heavily linked in the national media, when bookmakers began slashing the odds on Rooney becoming a Stoke player. But Scholes insists there has not been any contact with Rooney or his representatives.
“Wayne Rooney has been one of the best of his generation,” he added. “He has been and still is a great football player. But there’s been no conversations whatsoever about Wayne Rooney coming to Stoke.”