Tottenham have also been monitoring his situation with Mauricio Pochettino yet to make a signing in the transfer window so far.
Alexandre Lacazette and Sead Kolasinac have been recruited and the arrival of the Monaco star will be a huge boost for the Gunners, who would take their summer spending to £97m.
"We like Manchester United and the work of Mourinho, but we have a little soft spot for City", he added.
"Fabinho and Lemar are essential players, they will stay with us", Vasilyev insisted during a press conference held in the principality on Wednesday (26 July) to officially introduce new recruits Terence Kongolo, Diego Benaglio, Soualiho Meite, Youri Tielemans and Jordi Mboula.
Monaco's recruitment drive has been focused on defensive areas with the additions including combative midfielder Meite from Zulte Waregem, centre-back Terence Kongolo, and goalkeeper Diego Benaglio.
Finally, according to The Independent, Jack Wilshere wants to remain close to London if he moves on from Arsenal.
The 21-year-old can play anywhere across the midfield, can play with both feet, and his passing is exceptional.
"Fabinho has also publicly stated that he would be open to the transfer".
The French club have struggled to tie down some of their finest talents this summer following their impressive performance last season where they outshone Paris Saint-German by winning the Ligue 1 title.