Alonso was always open to moving to London and working at Chelsea, and is understood to be highly enthusiastic about the role.
He is keen to relocate and ready to return to a top-level club job, six months after his departure from Real.
Any initial concerns during early negotiations about the much-criticised BlueCo project have now been allayed.
Alonso had been linked with a potential move to Liverpool, where he spent five seasons as a player, in recent weeks – with the pressure on Arne Slot increasing following a disappointing season.
It remains a tough task to galvanise Chelsea in a season in which two permanent head coaches left the club.
Players have been accused of downing tools, while Marc Cucurella and Enzo Fernandez have appeared openly critical of the project in interviews in their native language.
It is hoped Alonso will have the personality, gravitas from his playing career and tactical acumen to bring the club back to the standards it expects by qualifying for the Champions League and winning trophies.
He may have to do so without European football, with Chelsea ninth and needing to finish at least eighth to qualify for the Conference League – after missing the chance to reach the Europa League by winning the FA Cup.