The 31-year-old has been a free agent since leaving Nottingham Forest last summer, and he has been linked with a move to Saudi Arabia, while there have also been suggestions of interest from the MLS.
As it stands, Lingard is still a free agent, but according to talkSPORT, he could be handed the chance to return to the top flight of English football with Everton.
The report claims that the Toffees are preparing to offer him the opportunity to sign a contract at Goodison Park until the end of the 2023-24 campaign.
Lingard started his professional career with Man United, representing the Red Devils on 232 occasions, but he left the club on a free transfer at the end of the 2021-22 campaign.
The forward became Forest's highest-paid player when he arrived at the club in July 2022, but he left after just one campaign, having failed to make his mark at the City Ground.
Staying in the Premier League, Sheffield United are reportedly pushing to sign Ben Brereton Diaz on loan from Villarreal for the second half of the 2023-24 campaign.
The 24-year-old made the move to the Yellow Submarine last summer after running down his contract at Blackburn Rovers, and he has made 20 appearances for the La Liga side this season but is yet to register a goal or an assist.
According to the Daily Mail, Sheffield United, who are bottom of the Premier League table, have identified Brereton Diaz as a target during the January market.
The Chile international scored 47 goals and registered 16 assists in 177 appearances during his time at Blackburn, including 45 goals and 14 assists in 160 Championship outings.
Sheffield United are rooted to the bottom of the table on nine points, seven points from the safety of 17th position, and they are expected to be busy during the January market.
Meanwhile, according to the London Evening Standard, West Ham United defender Thilo Kehrer is nearing a loan switch to Ligue 1 outfit Monaco.
The 27-year-old made the move to the Hammers from Paris Saint-Germain in August 2022, and he made 38 appearances for the capital outfit last term.
Kehrer has only featured 12 times for David Moyes's side this season, though, with just four of those outings coming in the Premier League.
The report claims that Monaco are nearing a loan deal for the defender, who needs regular action in the second half of the season to stand a chance of making the Germany squad for Euro 2024.
Roma have also been credited with an interest in Kehrer, but Monaco seemingly lead the race, and the Ligue 1 side will allegedly have the chance to sign him on a permanent deal at the end of the 2023-24 campaign.