The Argentina international is expected to play a central role under the newly-appointed Hammers boss whose side have dropped into the Premier League's bottom three.
But The Mirror understand Tottenham boss Mauricio Pochettino is a big fan of Lanzini and is keeping tabs on the playmaker as the new era at West Ham begins.
Relations between West Ham and Tottenham are not said to be good and they would be further inflamed should Lanzini swap his current employers for north London.
But as the Brazil international's attempt to move to Barcelona was blocked amid multiple bids from the Catalan giants, West Ham began attempts to keep Lanzini from leaving.
Reports in August claimed that West Ham were preparing a offer a bumper new contract worth £85,000-a-week, which would see him earn £4.4m a season, in an effort to warn off Liverpool and other potential suitors.
But amid the east Londoners' poor start to the campaign and Slaven Bilic's dismissal as manager those talks have subsided leading to fresh scrutiny over the two-and-a-half seasons remaining on his contract.
Everton, Liverpool's Merseyside rivals, also enquired over Lanzini's availability but then-manager Ronald Koeman eventually moved to Swansea City's Gylfi Sigurdsson.
Despite being seen as a central figure at the London Stadium, Lanzini's contribution to the club during his 30 months in England has been relatively modest.
In 77 appearances in all competitions Lansing has made eight assists and scored 16 goals, though one of those came at White Hart Lane against Tottenham and worked to alert Pochettino over his potential.