The 20-year-old established himself as a regular fixture in Jocelyn Gourvennec's midfield last season with three goals and an assist from 42 games in all tournaments.
Onana only arrived at the club from Hoffenheim in the summer of 2021, and his contract at the Stade Pierre-Mauroy does not expire until 2026.
According to The Athletic, West Ham tested the waters with a £19m bid for Onana, but their advances were swiftly rebuffed by Lille, who insist that the Belgium international is not for sale.
Arsenal are also said to hold an interest in signing Onana, but West Ham could yet return with an improved offer for the Lille lynchpin.
As well as seeking out more midfield reinforcements, West Ham boss David Moyes is known to be on the lookout for a striker to help take the pressure off of Michail Antonio's shoulders.
Chelsea youngster Armando Broja has been mentioned as a possible target, with the Albania international hitting six goals in 32 Premier League games during a loan spell at Southampton last season.
According to the Daily Mail, West Ham have now officially registered their interest in signing Broja, but they will need to fend off competition from Everton in order to do so.
The report adds that Thomas Tuchel wants to assess Broja in pre-season before making a decision on his future, and a fee of £30m will likely be required to sign him.
Broja has four years left to run on his contract with Chelsea but has only made one senior appearance for the Blues so far.
Over at the City Ground, Nottingham Forest have wasted no time in bolstering their squad for the 2022-23 season after earning promotion back to the Premier League under Steve Cooper.
Taiwo Awoniyi, Giulian Biancone and Dean Henderson have both arrived at the club, and Mainz 05 defender Moussa Niakhate could soon follow suit.
According to the Daily Mail, a £13m agreement is in place between the two clubs, and Niakhate should be unveiled as a Nottingham Forest player this week.
Niakhate is understood to have already completed his medical with the Tricky Trees and will leave Mainz after a four-year spell at the Bundesliga club since arriving from Metz.
The 26-year-old wore the captain's armband for Mainz in the 2021-22 season and found the back of the net four times in 30 top-flight games for the club.
Finally, Manchester City's search for new talent is supposedly set to lead them to Germany, where 17-year-old Dzenan Pejcinovic resides.
The 2005-born attacker previously spent time at Bayern Munich before joining Augsburg's youth academy in the summer of 2017, but he is now a free agent.
According to German outlet Bild, Man City boss Pep Guardiola is keeping tabs on Pejcinovic's development after the teenager hit 12 goals in 16 Under-17 Bundesliga games last season.
The 6ft 2in striker has also racked up a remarkable 17 goals and five assists in 16 games for Germany's Under-17s and has also captained the side on two occasions.
However, Wolfsburg are thought to be leading the race to sign Pejcinovic, while Juventus are also monitoring the situation closely.