The 23-year-old Uruguayan has been dubbed 'the new Luis Suarez' and won the Golden Boot in the 2020 MLS Is Back tournament with seven goals.
Rossi has emerged as one of the top young players in the MLS and is a accomplished finisher.
While he is yet to receive full international recognition with Uruguay - having so far represented his country at Under-15 to Under-21 level - he is highly-rated with a call up expected soon.
Most recently Armenia, his mother's place of birth, have failed in their attempts to get Rossi to switch international allegiance, while he is of Italian descent through his father's side.
Rossi, who is valued around the £10million mark, has been a big hit in America since arriving in 2017 from Uruguayan club Penarol.
The young forward has spent four seasons in the MLS having joined LAFC ahead of their first campaign as a new franchise, and scored the club's first competitive goal in their history in his MLS debut against Seattle Sounders.
In July 2020, Rossi also scored four goals in a 6-2 victory in a local derby against LA Galaxy - dubbed El Trafico - in a MLS is Back Tournament.
Rossi has a record of 56 goals and 21 assists in 107 games for the California club.
Everton are looking for attacking reinforcements this summer having released Josh King, who they only signed from Bournemouth in January, while Spurs are also on the hunt to add to their frontline.