The England international's fortunes at Old Trafford did not improve last season, and he is now officially a free agent after his contract expired at the end of June.
West Ham United are thought to be keen to welcome Lingard back to the English capital, while Everton have also been credited with an interest in the attacker.
According to Football Insider, Lingard has now let it be known that he expects to sign a £150,000-per-week deal, and Everton may be in a better position to bow to his demands.
The 29-year-old hit nine goals and five assists in 16 Premier League appearances for West Ham during a brief loan spell in 2021, helping the Hammers qualify for the Europa League.
Meanwhile, Nottingham Forest's busy summer of spending has already seen them welcome Dean Henderson and Taiwo Awoniyi to the club, and Neco Williams could soon follow suit.
The Wales international helped Fulham achieve promotion to the Premier League last season, but the Cottagers are fighting an uphill battle to sign the right-back permanently.
A separate report from Football Insider states that Forest and Williams have now come to an agreement over personal terms, but the Tricky Trees are still working on a fee with Liverpool.
The Reds are said to be holding out for a fee of £15m for Williams, who is determined to join Steve Cooper's side and play in the Premier League regularly.
However, having already seen a bid of £12m rejected, Forest could supposedly drop their interest in the 21-year-old and prioritise their pursuits of other targets.
Down on the South Coast, Southampton - who are reported to be another potential suitor of Williams - are seemingly closing in on their fourth signing of the summer window.
Gavin Bazunu, Mateusz Lis and Armel Bella-Kotchap have all arrived at St Mary's in the past few weeks, and another Manchester City player could now don the red and white next term.
According to transfer expert Fabrizio Romano, the two clubs have now reached a full agreement over a deal for Romeo Lavia, who will cost the Saints £10m.
Romano adds that City will insert a buy-back clause into the 18-year-old's deal, and he leaves the Premier League champions two years after signing from Anderlecht.
In that time, Lavia has made two senior appearances for Man City in the FA Cup and EFL Cup, while he scored one goal and set up two more in 20 Premier League 2 appearances last term.
Over in Italy, Roma starlet Nicolo Zaniolo has endured a frustrating period of development with injuries, but the 23-year-old avoided any serious problems and made it count in the 2021-22 season.
Under the wing of Jose Mourinho, Zaniolo struck eight goals and provided nine assists in 42 games across all competitions, including the winner against Feyenoord in the Europa Conference League final.
Zaniolo has two years left to run on his contract with Roma, but according to journalist Nicolo Schira, Juventus are now preparing an official offer for the Italy international.
Tottenham Hotspur and Newcastle United have previously been linked with a move for Zaniolo, who will supposedly command a €50m (£42.9m) figure to leave Roma.
Zaniolo has 22 goals and 15 assists to boast from 111 games in a Roma shirt, but he missed the entirety of the 2020-21 season with his second cruciate ligament rupture.