The 20-year-old endured a difficult first campaign at Goodison Park last season following his £10m move from Hadjuk Split. The Croatian made only 12 Premier League appearances and failed to score in any of them as the Toffees finished 8th in the table. He did, however, manage to score twice in six Europa League appearances for the Merseyside club last season.
And the Daily Mail claim that Rafa Benitez's Newcastle side have begun talks with Everton about taking Vlasic on a temporary deal for the forthcoming campaign.
The attacking midfielder, who can also play out wide or up front, has been playing for the Toffees during their pre-season friendlies, as Marco Silva looks to assess Vlasic ahead of his first season in charge of his new club.
The Croatian could become the Magpies' fourth signing of the summer following the arrivals of Swansea's Ki Seung-Yeung, winger Kenedy from Chelsea and the permanent signing of goalkeeper Martin Dubravka after a successful loan spell at St. James' Park last season.
Yet Benitez is expected to continue spending as West Brom's Salomon Rondon and Mainz defender Yoshinori Muto are also being lined up as potential arrivals, according to the Mail.
Vlasic's arrival in the North East could spell the end of Matt Ritchie's time at Newcastle, who is widely expected to join Championship side Stoke City during this window. The Scotland international is seemingly deemed surplus to requirements at St. James' Park despite making 35 Premier League appearances for the Magpies last season.
Newcastle have also shown an interest in bringing back Andros Townsend to the club, after the England international left for Crystal Palace two seasons ago. It is unclear as to whether Vlasic would be brought in as an alternative option to Townsend, or if he would be bought alongside the Eagles player.