Those at Stamford Bridge are hoping to discover that their star player wants to stay put.
Richarlison is now in his second season in England, having made his way to Watford from Fluminense in the summer of 2017.
The Italian global remains a key figure for the Partenopei, having scored 11 goals and provided six assists in 27 appearances so far this season.
Any movement on these deals would of course hinge on Hazard's exit from Stamford Bridge.More news: How Manchester United could line up against Fulham
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Eden Hazard has said he has made a decision on his Chelsea future, but has not expanded on what it is.
Marcus Rashford: Manchester United want to get the 21-year-old tied down to a new deal this season to keep Real Madrid at bay, The Sun reports. Richarlison is one such option. "I have decided", said the 28-year-old Belgian worldwide.
Coutinho has endured a tough time at Barcelona so far and Maurizio Sarri's side could offer him a potential escape route at the end of the season.
The problem though, is that Brazilian forward has been quite inconsistent for both Everton and Watford, although his in-form periods have been more outstretched at his current club, which is a positive.
Chelsea signed American worldwide Christian Pulisic in a £58m deal from Borussia Dortmund in January, but he is expected to be a long-term replacement for either Pedro or Willian on Chelsea's right flank with both players in their 30s.