However, Tottenham deny having made contact with Conte or any other prospective post-Redknapp candidates.
It is said their recruitment procedures will only get under way once the Football Association’s intentions over the England vacancy become clear.
Indeed, Redknapp’s status as the bookmakers’ favourite for that role appeared at least initially to destabilise his squad following Fabio Capello’s resignation in February.
If Wembley’s supposed interest in Redknapp materialises into a job offer, there is no guarantee that – having vacillated between enthusiasm and doubt about the England job – he would accept it.
In that event, or if no FA offer were made, Redknapp will remain Spurs manager into next season. Otherwise, Spurs expect that, if their manager does leave, the vacancy would attract significant interest from leading managers.
That much has been signalled by the number of approaches the Spurs chairman, Daniel Levy, has received amid the England speculation surrounding Redknapp.
Everton’s David Moyes has been linked with the role, as has Brendan Rodgers, but the Swansea manager said yesterday he was in no rush to leave the Liberty Stadium.
He has won rave reviews this campaign for his side’s Barcelona-style passing game.
“I take great satisfaction in my job here and it’s nice and humbling whenever people are saying nice things about you,“ said Rodgers, “but for me there are many great managers at this level.
"My only concentration and focus is on our next game and trying to make sure that we can maintain the standards that we have set all season.
“I have been here a couple of seasons and we have had success here. There is always gossip and speculation, which you can’t do much about, but I love it here and hope to continue.”
Meanwhile, Rodgers believes Premier League player of the month Gylfi Sigurdsson is Swansea’s very own Frank Lampard. The 22-year-old Icelandic midfielder, who is on loan from Hoffenheim, scored his sixth goal in 11 league games against Spurs on Sunday.
“It is a great honour for him and shows the level the team have been at as well.” said Rodgers. “He has been a wonderful acquisition, I knew what I was getting and he has delivered brilliantly.
"Hopefully he can continue that until the end of the season.
“He is in the Frank Lampard mould, he gets into the six-yard box, is willing to get his shot off and can score with his head like he did at Fulham.
"I’m not saying he is as good as Lampard but he is that type of goalscoring midfield player.”