Patrick van Aanholt was undertaking a medical at Crystal Palace on Friday ahead of a proposed big-money transfer from Sunderland.
Palace manager Sam Allardyce confirmed the development, and also refused to rule out a further attempt to sign Arsenal's Carl Jenkinson before Tuesday's transfer deadline.
Press Association Sport understands Sunderland have agreed to sell left-back Van Aanholt, who played for them under Allardyce last season, for a fee which could rise to £14million.
Allardyce credits Van Aanholt with playing a significant role in Sunderland's unlikely successful survival bid last season, and is also unconcerned about the 26-year-old defender's heart, after a scare in September.
"It won't go through until we have every aspect of negotiation, or what the medical might say," said Allardyce, whose team on Saturday host Manchester City in the fourth round of the FA Cup.
"It's in the process at the moment.
"We've had many players with a similar condition; it's quite common throughout the game, it's just a precaution we have to take.
"I wouldn't imagine (the heart issue) will be a problem. I've had two players in the past with a very similar condition. I'm sure the medical will be okay and that Patrick will be looking forward to joining us."
Van Aanholt was withdrawn from the line-up Sunderland named at Tottenham in September just 15 minutes before kick-off after a phone call from a cardiologist to their club doctor.
He has since been a regular and according to Sunderland chief executive Martin Bain has told them of his plans to leave.
"He was a major saviour in our run last season," said Allardyce. "He was a major part of that success story.
"His contribution, in terms of assists and goals, was massive. When it came to defending he got better with me and listened to what we told him about where the weaker side of his game was and he made it stronger.
"(He provides) great energy, a very good player. He and (Jeffrey) Schlupp will increase the speed and energy levels of the squad. If everything goes well, I look forward to him joining me again."
Progress has been made in the pursuit of Van Aanholt since Palace were unable to agree terms with fellow full-back Jenkinson, but when asked if that transfer could be revived, Allardyce said: "Maybe. There are several we're hopeful for between now and Tuesday.
"But there are many deals we haven't got that we've tried to do, and this one - Carl - there has been a stumbling block. That has been the biggest blocker of transfers in this window; it's become very expensive to do business."
It had also been reported Palace had made bids for Norwich's Robbie Brady and Lille defender Ibrahim Amadou, but Allardyce said "They are not in our process at the moment."
He also insisted Palace had received only loan enquiries for their players, despite reports of a potential return to France for Yohan Cabaye or a switch back to Newcastle for Andros Townsend.
Allardyce also again spoke of the fact Palace's battle to avoid relegation is a greater priority for him and his team than the FA Cup.
Against City he remains without Julian Speroni and Scott Dann, owing to respective knee and hamstring injuries, but with Fraizer Campbell and Steve Mandanda back in training the Palace manager said he will pick his strongest team.