The Spaniard has been out of work since being sacked by Real Madrid in January, but is ready to take on his next challenge.
Chelsea have placed him at the top of their shortlist and want to make their appointment before the World Cup kicks off in mid-June.
According to The Independent, Alonso is "understood to see many attractive elements in the job", including the current squad largely fitting his footballing philosophy.
Conversely, the 44-year-old also wants assurances that he can build a project at Stamford Bridge, something Enzo Maresca felt wasn't possible under BlueCo's ownership.
Nonetheless, it appears a deal is edging closer to be completed, as Florian Plettenberg states there are "concrete talks" going on in the background and there is "growing confidence" he will become their next manager.
While accepting luring him to West London will be "difficult", Alonso isn't blessed with options currently, and may see a switch to Chelsea as a way into the Premier League.
The Blues play Manchester City in the FA Cup final later today.