Lanzini has been a revelation since signing for the Hammers during the summer transfer window, and he has earned a number of plaudits for his performances.
However, Thompson feels that Allardyce would have been more reluctant to play the Argentine attacking midfielder than Slaven Bilic, due to his slender frame.
“He’s another frail boy, who might not have got a chance in this side under Allardyce,” Thompson said.
“Lanzini has this great quality – he has the final ball, he has an end product to his game. And in a game which is very close, when you have the Lanzini in [Dimitri] Payet you can always get a point out of nothing.”
Lanzini has been one of West Ham’s standout players so far this season, and he has scored on a regular basis since arriving at Upton Park.
The 22-year-old has netted four times in 11 matches, and he has been given a key role in West Ham’s team by Bilic.
Lanzini was one of the few West Ham players to come out of yesterday’s 4-1 defeat against Tottenham Hotspur with any credit, after he scored a late consolation, and it will be important that he keeps his good form up.
The Hammers have been dealt a big blow, after Dimitri Payet picked up an injury, and there is pressure on Lanzini to feel the void the French international’s absence leaves.