The 26-year-old centre-back joined Chelsea's academy at the age of eight and progressed through the club's youth ranks alongside older brother Nathaniel, also a professional footballer.
Chalobah spent time on loan at Ipswich Town, Huddersfield Town and French side Lorient before establishing himself at Stamford Bridge, making his senior debut in the 2021 UEFA Super Cup victory over Villarreal.
He scored on his Premier League debut against Crystal Palace that same month, and has since gone on to make over 100 appearances for the club, representing England at senior level and signing a contract extension that runs until 2028.
Cesc Fabregas's side are planning to increase their bid for the defender to £25.7m (€30m), plus a further £4.28m (€5m) in potential add-ons.
Chelsea, however, have been holding out for a total package closer to £30m (€35m) for the centre-back.
Como's opening offer had fallen short of that valuation, coming in at just over £23m including add-ons.
The Serie A club also face competition from Inter Milan, who are weighing up a bid of their own for the same player.
Chalobah's situation remains unresolved as the two Italian clubs continue to monitor developments, with Chelsea yet to indicate which offer, if any, meets their asking price.
Como are keen to strengthen their backline following promotion, and see the England international as a player capable of adding both Premier League experience and versatility to Fabregas's defence.
Any deal would represent a significant departure for Chelsea, who have relied on Chalobah as squad cover across multiple positions in defence in recent seasons.