Blues boss Antonio Conte is interested in the 23-year-old, who only joined Genoa from Inter Milan on a permanent deal in the summer.
But he faces competition from the Gunners with Tuttomercatoweb claiming Laxalt has caught the attention of their scouts.
“There are many clubs that have been scouting him”
Uruguay international Laxalt spent last season on loan at Genoa and provided three goals and four assists in 35 appearances to help the club to 11th in Serie A.
The 23-year-old has one goal and two assists in the current campaign.
He is under contract until 2018 and his agent Vincenzo D’Ippolito admitted a number of vultures are circling.
“There are many clubs that have been scouting him,” D’Ippolito told Italian publication CalcioMercato.
“Fiorentina have been watching him for very long time, they also wanted to sign him last summer, but there are requests also from the Premier League.
“Conte had been scouting Laxalt when he was in Italy and he’d love to take Laxalt to Chelsea now.”
Chelsea could step up their search for Laxalt if Oscar completes his £60m move to Shanghai SIPG.