Juventus plan Robin van Persie, or Luis Suarez for their attack
The Serie A champions have had an initial enquiry rebuffed by Arsenal, who also dismissed an opening formal bid from United out of hand on Friday.
United's bid is believed to be around £10m, £15m below Arsenal's valuation.
Arsenal boss Arsene Wenger has repeated his desire to keep Van Persie.
"For me, Van Persie is one of the best strikers in the world, if not the best, and I want to keep him at the club," Wenger told Arsenal Player.
"As for the rest I will do what is in the best interests of Arsenal Football Club. That, at the moment, is where we are. There is not a lot more to say than that."
Sir Alex Ferguson“We've shown an interest and that's where we're at at the moment”
The Gunners' 28-year-old captain has a year left on his contract with all three interested clubs offering lucrative financial packages, more than doubling Van Persie's current wage.
Van Persie scored 41 goals in 53 games for club and country last season and was named Professional Footballers' Association and Football Writers' player of the year of playing alongside Suarez that could sway his thinking.
If Juventus can secure a deal for Van Persie they will turn their attentions to Suarez and intend to raise the necessary funds by selling striker Alessandro Matri to AC Milan.
Liverpool will take a dim view of Juventus's interest in Suarez and have no intention of allowing their prized Uruguayan forward to leave the club.
Suarez is under contract at Anfield until 2016 - but the Reds are keen to tie him down to an even longer deal.
