New Blues boss Antonio Conte has previously worked with the 27-year-old during his time at the Serie A giants - where he led the club to three successive title triumphs - but a fee of 20 million Euros (£15.7 million) could be enough to allow the Italian Champions to part with the player.
There will be something of a worry in terms of the amount of playing time Asamoah had last season, given that he only made 13 appearances in all competitions because of one or two injury problems during the season.
It should be of little surprise that Chelsea are linked with a player who used to work under their incoming manager, as he will look to build a side that can adapt to his ideas as quickly as possible.
So signing a player that he has previously worked with will be the kind of thing any manager would do in order to try to get their ideas across as quickly as possible.
One wonders after a season when injuries have been something of a problem for the player that he will be a signing for the long-term, but certainly one that might be able to have a significant impact in the next couple of years.
There have been a number of players linked to Chelsea already this summer, which suggests that Conte is keen to put his own stamp on this team as soon as possible, and maybe use the time on the training ground that is afforded to them without European football this season to really make their mark.