Conte is being hotly tipped to succeed interim boss Guus Hiddink in the summer. Gary Stonehouse of the Sun reported on Monday that Blues owner Roman Abramovich wants to shake hands on a deal for former Juve chief Conte to assume control next season.
Conte will apparently be expected to take over once he fulfils his obligations with Italy at UEFA Euro 2016. If that happens, he could make a move for Atleti's free-scoring talisman.
Italian source Calciomercato (h/t Metro's Max Miller) claimed Conte wants the player valued at "£38.6 million" to bolster the club's forward options. Griezmann is certainly talented enough to do that.
As a roving forward who boasts some of the most perceptive movement in Europe, Griezmann has helped himself to 21 goals in all competitions, per WhoScored.com.
The former Real Sociedad man has excellent timing with his runs, can finish with either foot and is deceptively effective in the air. Given the right service, Griezmann is a lethal match-winner who guarantees goals.
Links between the gifted Frenchman and Chelsea have been fairly consistent this year. In late January, Rob Draper of the Mail on Sunday suggested the Blues were keen on Griezmann as a possible alternative to Belgian winger Eden Hazard.
Griezmann would certainly offer a greater goal threat than Hazard, but he isn't the only French star Conte could target, according to reports.
Blaise Matuidi on the Radar
The report claimed Conte is a fan but that PSG won't be in a mood to sell:
Antonio Conte, who is set to become manager at Stamford Bridge, is understood to be an avid admirer of Matuidi and has placed the France international at the top of his transfer shortlist.
However, PSG do not intend to part with the midfielder so the Blues may have to break the bank to force their Champions League rivals into selling.
Yet, to "break the bank" for Matuidi is a move worth making. He's perfect for the intense pace and combative style of play in England's top flight.
Few midfielders can match the engine Matuidi boasts. He covers ground relentlessly to make himself a force in either box. It's a quality that makes him a great transition player, one able to link possession all over the pitch as well as start and dictate swift breaks.
If Chelsea were to place Matuidi between a holding player such as Nemanja Matic and a playmaker as creative as Cesc Fabregas, they'd have close to the perfect midfield trio.
Dominance of the middle was a signature of Conte's during his time with Juve, when Andrea Pirlo, Arturo Vidal and Claudio Marchisio routinely bossed games for the Old Lady.
Should Chelsea spend big on Matuidi?
Signing Matuidi would make similar dominance possible for Chelsea.
Of course, all of these rumours come with the rather large caveat of Conte's still unresolved future. But even if the Italian doesn't commit to taking over, Griezmann and Matuidi represent excellent targets in the summer window.
Signing both would put the Blues back at the forefront of the title mix next season.