The midfielder is set for a return to Manchester in pre-season having played his final game for the Hammers on Sunday, helping the club to secure a sixth-placed finish in the Premier League and European football for next season following a 3-0 win over Southampton at the London Stadium.
It concludes a successful loan spell for Jesse, who has been able to combine regular minutes on the pitch with a return to both the goal and assist columns.
The 28-year-old originally joined the Hammers in January and was reunited with former Reds manager David Moyes in his search more frequent first-team football, having only featured three times for United in the first half of the campaign.