Chelsea are pushing to completing a deal that will see Rennes goalkeeper Edouard Mendy.
The FA Cup finalists previously tabled a bid to the Breton side for €20 million (£18m/$24m) but found the French club stubborn in their resistance to letting their No.1 depart for such a fee.
With a desire to complete a deal this week, they are willing to push for any fee up to €28m (£25/$33m) before bonuses in order to reach an agreement.
The Blues have been following the shot-stopper for an extended period and were also linked with Lille's Mike Maignan for the role.
Mendy spent last season in impressive form for the Breton side and helped them qualify for the Champions League for the first time after a third-place finish in Ligue 1.
Meanwhile, winger Kenedy has arrived at Granada for his medical ahead of a season-long loan deal as Frank Lampard seeks to cut down his squad having made a host of big signings.
The 24-year-old is set for his fifth loan move having spent last season in La Liga with Getafe and remains under contract at Stamford Bridge until 2022.
On the other hand, the Emerson Palmieri talks with Inter have not progressed quickly as the Serie A club are suspected to be waiting until the end of the window to drive down the Blues' £26m ($35.5m) asking price.
Chelsea have had interest registered in Michy Batshuayi from West Brom, while their talks with AC Milan over Tiemoue Bakayoko's loan move continues to progress slowly.
Milan are hoping to conclude a deal that includes a €3m (£2.7m/$3.55m) loan fee and a €30m(£27m/$35.5m) option to buy, but the London outfit are keen to force the Italian giants into an obligatory purchase option at the end of the season.
Atalanta have registered an interest in loaning full-back Davide Zappacosta but no deal is close with the Bergamo club weighing up a number of options including Valencia's Cristiano Piccini.
Chelsea are having another busy week in their efforts to reduce the size of their squad which sees them with almost 50 players on their books after five high-profile signings.
Conor Gallagher remains in talks over a new contract, with a loan move to Premier League side Crystal Palace being lined up.
The Blues continue to stall on Fikayo Tomori's future, despite Premier League clubs joining Rennes with an interest to loan the central defender.
Ethan Ampadu, Malang Sarr, Matt Miazga, Baba Rahman, Dujon Sterling, Nathan Baxter and Jake Clarke-Salter all have advanced talks open over various loan deals away from the club.
Tariq Uwakwe was the latest player to agree on a loan deal, having signed on loan at League One Accrington Stanley from the Under-23s squad.
Meanwhile, Kai Havertz, who arrived in a £70m ($91m) deal on Friday from Bayer Leverkusen, is competing for a starting spot against Brighton on Monday in the first Premier League game of the season.
He has impressed Frank Lampard and his coaching staff with his fitness levels since signing for the club after being allowed to leave the German national team early to begin life at his new club.
Fellow new signing Ben Chilwell looks unlikely to make the club's first two matches of the season as he continues to recover from a heel injury.
The former Leicester defender has been doing solo sessions with ball work ahead of the new campaign which has given staff a boost that he will soon be ready for action.
The status of Christian Pulisic and Cesar Azpilicueta remains unclear ahead of the new season after injuries in the FA Cup final defeat to Arsenal last month.
Finally, Hakim Ziyech picked up a minor injury in the club's only pre-season friendly against Brighton and his fitness remains in doubt.