Conte, who revealed he attempted to sign Sanchez while at Juventus, believes the 29-year-old is one of the top players in the world and admits he is a big fan of the former Barcelona forward.
Sanchez was subject to a £20M enquiry from Man City earlier in the transfer window, but Arsenal will not sell to a Premier League club for less than £35M.
Cole, who played for United between 1995 and 2001, believes buying Sanchez would be a good deal for Mourinho's side.More news: Trump Gives The Iran Deal One Last Lifeline
Arsene Wenger concedes that Alexis Sanchez is likely to leave Arsenal, but he remains optimistic regarding a new contract for Mesut Ozil. While there is a no way to go before Malcolm is confirmed as an Arsenal player, based on his Instagram pictures showing him learn English its fair to say that the Brazilian will be making a move to the Premier League soon. We don't believe in signing a player just to sign a player.
"But if there is a fantastic opportunity on the table, you fight for that fantastic opportunity".
United boss Jose Mourinho said Sanchez is a "phenomenal player" on Friday.
"These guys want to make money but they want to win trophies as well, so it is a combination of things".More news: Zuma booed by ANC members
With Antoine Griezmann too lurking around in the Red Devils' radar, Ed Woodward is reportedly determined to introduce a global superstar to Old Trafford by the end of the season.
Press Association Sport contacted both United and Arsenal with the Manchester club saying they were not aware of any bid for Sanchez while the Gunners declined to comment. Speaking on the possibility of the Chilean coming to the club, Manchester City winger Leroy Sane said he is not anxious about his place in the team.
Chelsea boss Antonio Conte has spoken of his admiration for Arsenal forward Alexis Sanchez, who he almost signed while managing Juventus. However, he and his agent are understandably considering United's offer, and any deal could depend on Arsenal securing a replacement, with Bordeaux's Brazilian forward Malcom said to be their main target.More news: A Selection Of The Most OTT Reactions To An Imagined Oprah Presidency