The Blues have identified Dewsbury-Hall as a key target this summer, with new manager Enzo Maresca keen to reunite with a player he managed at Leicester.
Dewsbury-Hall has made over 100 league appearances for Leicester and helped the Foxes win the Championship last season and secure an immediate return to the Premier League.
The 25-year-old midfielder is said to be open to leaving his boyhood club this summer and favours a move to Chelsea over Brighton, who have also expressed interest in securing his signature.
Chelsea reportedly submitted a bid to Leicester on Friday and have indicated they are willing to send one of several players the other way if it means bringing Dewsbury-Hall to Stamford Bridge.
The Daily Telegraph say striker Armando Broja, forward David Datro Fofana and midfielder Cesare Casadei – who spent last season on loan at Leicester – have all been raised by Chelsea as possible makeshifts in the deal.
Leicester value Dewsbury-Hall at around £35m and are under pressure to sell in order to meet profit and sustainability rules.
Championship-winning manager Maresca joined Chelsea after Mauricio Pochettino’s surprising departure from Stamford Bridge. The Blues finished sixth in the Premier League last season.
Blues striker Broja has scored just three goals in 38 appearances for Chelsea and was injured for most of last season. Despite his recent struggles, multiple Premier League clubs – including Everton – are monitoring his situation this summer.
Fofana, meanwhile, looks set to leave Chelsea just 18 months following his arrival at the club and has attracted interest from several European clubs.
If Chelsea reach an agreement to sign Dewsbury-Hall, speculation would only increase that Conor Gallagher – currently with England’s Euro 2024 squad – may leave the club amid interest from Tottenham and Aston Villa.
Speaking about his future this week, Dewsbury-Hall insisted he was ‘happy’ at Leicester, the club he joined at the age of eight.
‘I have been here since I was a kid,’ he told BBC Sport. ‘I love everything about the club. I grew up and managed to play in the first team.
‘I am happy. I have never said I am actively wanting to leave. That sort of stuff is not up to me. You never know with football – the season is about to start, so we will see.’
On Maresca’s move from Leicester to Chelsea, he added: ‘Enzo was an unbelievable manager. I genuinely see him becoming a top manager, so it wasn’t a surprise to see he was in demand.
‘It is weird having to change a manager after being so successful, but that’s football.’