Blues head coach Thomas Tuchel frequently insisted during the closing months of last season that he would hold conversations with the Spaniard this summer.
Arrizabalaga, a former club-record signing, is said to be keen on becoming a first-choice stopper elsewhere having remained as understudy to Edouard Mendy.
According to the Daily Mail, Napoli have asked Chelsea whether they would be willing to loan out the 27-year-old for the 2022-23 campaign.
The Premier League giants will only give consideration to such a proposal if they are able to sign a replacement, with Marcus Bettinelli due to remain as third choice.
Gabriel Slonina will stay at Chicago Fire on loan, even if Chelsea complete a deal for the teenager in the coming weeks, while previous target Thomas Strakosha has already signed for Brentford.
Manchester United have recently signed Lisandro Martinez from Ajax, the versatile defender joining the list of big names at the back for the Red Devils.
Nevertheless, according to Tuttomercatoweb, Erik ten Hag may consider making another addition for that area of the pitch over the coming weeks.
The Premier League giants have allegedly been evaluating the possibility of bringing in Felix Uduokhai from Bundesliga outfit Augsburg.
The 24-year-old was restricted to just 13 appearances last season, but he remains highly-regarded in his homeland having represented Germany at the Olympic Games.
Uduokhai - a centre-back who can also play on the left and in defensive midfield - has two years remaining on his contract.
Meanwhile, Chelsea appear likely to part ways with a number of fringe players over the next weeks with Tuchel already having a bloated squad for the club's pre-season tour of the United States.
Although Ross Barkley played 45 minutes in the 2-1 victory over Club America, it is highly likely that the Englishman will eventually leave Stamford Bridge.
According to The Mirror, Aston Villa and Everton have both been offered the opportunity to sign the playmaker this summer.
Both teams are former clubs of the 28-year-old, who now has just one year remaining on his contract with the West Londoners.
Barkley was restricted to just 25 minutes of Premier League football during the second half of last season, that outing coming in the final-day dead rubber with Watford.
Keeping on the topic of potential incomings at Everton and the Toffees remain keen to add a fresh face on the flank after the departure of Richarlison.
If reports are to be believed, Frank Lampard is keen on securing the signature of Maxwel Cornet, who contributed nine goals during his first year in the Premier League.
The Burnley wideman is said to have a release clause in the region of £17m, a fee which is yet to be met by Everton or any other interested clubs.
Nevertheless, according to the Daily Mail, Everton are preparing to make a fresh offer for the Ivory Coast international as they bid to strengthen their options ahead of the new campaign.
Burnley boss Vincent Kompany has already acknowledged that the player is likely to depart Turf Moor this summer.