Messi scored twice to take his tally to 100 goals in the Champions League as Barcelona thumped Chelsea 3-0 in the second leg of the round of 16 at Camp Nou on Wednesday.
Conte has one more season remaining on his three-year contract with Chelsea but he has indicated he is not entirely happy in London and misses Italy.
The man approached Conte at the front of the room on Thursday and spent around 30 seconds unchallenged while showing the Italian something on a tablet device.
Chelsea has lost three of its last four games in all competitions, and sits fourth in the league, a point above Tottenham.
Conte has been agitating and moaning for months about his failure to exert control, particularly over transfers.
Not being included in Chelsea's European squad means Costa will not be cup-tied for the tournament if he secures a mid-season transfer.
Everton offered little to show that it could win at Chelsea for the first time in the league since 1994, a run which now spans 23 matches.
With a 2-1 victory on Sunday secured through Marcos Alonso's double, the Premier League champions are finally up and running after a tough couple of weeks.
The English soccer season started last weekend but Costa is currently in his native Brazil, after claiming he was told in a text message sent by Conte during the offseason that he was not wanted at Chelsea anymore
The Portuguese having coached Matic earlier in Chelsea admitted that the Manchester club will help him grow better.
Manchester United have signed Nemanja Matic for 40 Million Euros from Chelsea as the Serbian was highly speculated on reuniting with his former boss Jose Mourinho.
Chelsea ultimately staved off the ignominy of being consigned to the lower divisions, finishing the 2015-16 season at a lowly 10th place.
Antonio Conte has signed the 24-year old for a club record on a Five-year deal at Stamford Bridge as Diego Costa is no longer a part of the manager's plan.
BPL winners Chelsea have finally roped in Bakayoko from Monaco who was highly speculated on snubbing the blues to join Manchester United.
2016-17 Premier League winners Chelsea are currently facing an innumerable amount of problems as the Blue's haven't landed any major signing yet for the season.
Former Blues striker and U-20 star Dominic Solanke will now play for the Reds at Anfield after Chelsea did not come to any conclusion for the forward
Milan, Dec 22: Juventus and Udinese failed to turn their attacking ambition into goals, playing out a 0-0 draw on Wednesday which leaves Antonio Conte's team level with AC Milan at the top of the
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