The attacking midfielder has been linked away from the club throughout the summer transfer window.
The Argentina international was linked with a potential move to Ligue 1 club Marseille earlier in the window.
Should West Ham Sell Manuel Lanzini?
It remains to be seen if an offer will be tabled but he has yet to make a start for the Hammers, with Pablo Fornals preferred in the number 10 role.
Said Benrahma and Jarrod Bowen have been used as the wingers, while Tomas Soucek and Declan Rice are immovable in central midfield.
But Rosser believes West Ham do have a role for Lanzini and will utilise him deeper in the side, meaning he will ultimately stay at the club.
He said: “I think Lanzini will stay now they’ve crafted this slightly deeper role for him.”
In total, Lanzini has made 158 appearances for the Irons since arriving back in 2016, scoring 22 goals and registering 23 assists.