The 18-year-old midfielder is highly regarded by the Citizens, who recruited the Belgium Under-21 international from Anderlecht in 2020.
Lavia made 27 youth appearances across all competitions in 2021-22 as well as two senior appearances for Pep Guardiola's side, but The Athletic reports that City are unsure as to whether he is ready to step up to the first team.
The report adds that Leeds and Southampton are interested in Lavia, and while Man City are reluctant to let the midfielder leave the club, he could be used as a makeweight in a deal to sign primary target Phillips.
The Citizens are believed to be the frontrunners to recruit the 26-year-old, who has allegedly told Leeds that he would like to move to the Etihad this summer.
Phillips is valued by the Whites at around £50m, but that price tag could potentially come down if Lavia were to move to Elland Road on either a temporary or permanent deal.
Lavia, who lifted the Premier League 2 title with Man City last season, has two years remaining on his contract.