The defender – whose loan at St James’s Park last season was cut short by injury – is out of contract at the end of the season.
Willems hasn’t played for Eintracht Frankfurt this season despite returning to fitness last year following knee surgery, and the 27-year-old has previously spoken about having unfinished business at St James’s Park.
Asked last summer if he was open to one day returning to Newcastle to finish what he started, Willems said: “Of course, of course. It’s sad that it ended like that. I feel like I’m not done yet. We will see. It would be great to be back and show them at St James’s.”
Steve Bruce last week revealed that the club, which signed three free agents last summer, will again be looking at Bosman signings in the summer window as it grapples with the financial impact of the coronavirus pandemic.
“Every club will be the same,” said United’s head coach. “They’ll be looking at Bosmans, which are always attractive for obvious reasons. But I have to say to everybody, I can't see there being swathes of money anywhere in the Premier League.
Newcastle’s interest in Willems comes amid questions over Matt Ritchie’s future.
The 31-year-old, under contract until 2023, returned to the starting XI as a left wing-back early last month, and has helped the club climb away from relegation trouble.
Ritchie – who was a target for former club Bournemouth in the previous two transfer windows – had previously been “frustrated” at a lack of starts.
“The situation we find ourselves in at the minute, and the system we’re playing, suits him very well,” said Bruce. “He’s very good at that.
"But he’s in an area and a position where we’ve got healthy competition. I’ll have discussions with Matt, but I’m delighted that he’s done exactly what we thought he would do.”
The decision to switch to a back five opened the door to a return for Ritchie as a wing-back, and Willems is well suited to this position. Bruce, however, has repeatedly stated his preference for a back four.