Quoting TuttoMercatoWeb in Italy, suggestions are that West Ham boss Manuel Pellegrini is planning to swoop for the versatile 25-year-old.
Laxalt impressed as part of the Uruguay national team at the World Cup this summer in Russia, and has put himself on the radar of a number of clubs. Everton are also known to be interested in the player, with Bournemouth also linked recently.
The Uruguayan is highly-regarded in Italy and can be deployed in a number of positions. Naturally playing as an attacking midfielder, Laxalt can also feature comfortably on the left flank - even filling in at full back for his national team during one match at the World Cup.
Laxalt joined Genoa as a permanent player in July 2016, but had previously been at the club on an 18-month loan from Inter.
During his time with I Rossoblu, Laxalt has made 111 league appearances and scored seven goals.
As a key player for Genoa, and given the significant interest in the player following the World Cup appearances, the Italian side are demanding that their asking price is met in full by any team wishing the sign the 25-year-old.
Laxalt has won 10 senior international caps since making his Uruguay debut in October 2016 in a 3-0 win over Venezuela.
The 25-year-old also helped his side score a second goal during their group stage match against hosts Russia at the 2018 World Cup - his deflected shot going into the net from Denis Cheryshev, who was credited with the own goal.
Laxalt finished as runner-up in the 2013 FIFA Under-20 World Cup, losing on penalties in the final to France.