Alonso has been busy in his opening weeks in charge at Stamford Bridge with Marc Cucurella, Tyrique George and Andrey Santos all moving on as Marco Palestra, Emmanuel Emegha and Geovany Quenda have all arrived.
The Chelsea hierarchy are hoping to offload several unwanted players, and Slonina is on that list, after not making a single first team appearance last season.
Slonina joined Chelsea from Chicago Fire in 2022, but despite being highly rated in MLS, the USA international has not been given a chance by several Blues bosses with loan spells out at KAS Eupen and Barnsley.
He is under contract at Chelsea until 2028, but with the club not looking to retain him, reports from French outlet L’Equipe have linked him with a move to sister side Strasbourg.
The deal could be a season-long loan or a full transfer as he heads for talks with Strasbourg head coach Hugo Oliveira.
If Strasbourg are unconvinced by Slonina, Chelsea could offer them another goalkeeper on the fringes of Alonso’s plans, with Filip Jorgensen also tipped for an exit.
If the pair both move on, that would leave Alonso with Robert Sanchez and Mike Penders as his two keepers for next season, unless he can persuade the club to pay out for yet another No.1.