The 44-year-old has become the favourite for the role at Stamford Bridge despite being let go by Real Madrid earlier this season after a tough spell with the Spanish giants.
Alonso guided Bayer Leverkusen to the Bundesliga title in 2023-24 as his side became the first ever club to avoid defeat in a top-flight season in Germany.
There is no doubt that he could have a serious impact on the club who are set to face Manchester City in the FA Cup final this weekend in what is there final chance to secure European football.
Speaking to Bet St George, Danny Mills suggested that Alonso may not take the job as the control he would demand from top to bottom is beyond what Chelsea would want in a manager.
“Someone like Xabi Alonso is going to want control, a big say in signings and how the team plays.
“I think we've seen over the last few seasons at Chelsea, since the new ownership group have come in, that won’t necessarily happen and, ultimately, that's why (Enzo) Maresca walked away.
“If Chelsea want a Xabi Alonso or a Pep Guardiola, they’ve got to change their plan completely and go: ‘Carte blanche, we are going to give you a huge say in recruitment, the style of play and the players that you want within this.’ Some of those players are going to be costly.”
Alonso has also been linked to the Liverpool job but with Arne Slot’s role secure, Chelsea may be his only option heading into the new season.