The forward has interest from clubs across Europe but his current side are holding firm over their transfer fee demands
Napoli have made an offer of £27m (€30m/$35m) already with further add-ons being put forward, while Rennes have only been able to put an £18m (€20m/$23m) offer in.
Chelsea’s approach for Rennes goalkeeper Edouard Mendy could see the Ligue 1 club earn up to £25m (€28m/$33m) for their current priority target with talks ongoing.
Rennes manager Julien Stephan recently spoke out about his admiration for Boga as the Ligue 1 side look to secure a deal.
“I can’t speak about numbers. He is quite simply a player who is coming out of a very good spell with Sassuolo,” Stephan told Telefoot.
“He has very interesting characteristics in terms of his penetration, his pace and his ability to finish off moves. We know him well at the club as he was on loan here a few seasons ago. At the time, I was in charge of the reserves, we got to know each other in certain instances, we know each other.
“He is a player who is one of our potential targets, there is enormous competition with very big clubs – we will see what happens in the coming weeks and months.”
Blues director Marina Granovskaia negotiated a change in clauses ahead of the transfer window, having had a buyback option on Boga.
The Serie A side are keen to keep a long term connection open with the Stamford Bridge outfit and the talks were concluded with ease.
Bayer Leverkusen are closely tracking the situation but are cautious about having to pay the sums that are being demanded by the Serie A side, even having received £70m (€75m/$90m) from Chelsea for star man Kai Havertz.
The interest in Boga has grown since his emergence as one of the best players in Serie A outside of the biggest group of clubs, after he scored 11 goals in 35 appearances last season in all competitions.