The club revealed on Friday that Chakvetadze would miss the opening weekend match at Charlton on Saturday as he awaits the results of a scan on a toe issue, an injury that has plagued him since he missed the final month of the 2024/25 campaign.
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There is no return date currently set for the Georgian, who had initially hoped to be available for the start of the season, with Pezzolano accepting he is an "important player" but that they must "follow the process" to get him fit.
Assistant sporting director Valon Behrami, who joined Pezzolano on press conference duties, added that Chakevetadze's rehab was going well and that his return is "a matter of time and patience".
Giorgi Chakvetadze is suffering with a toe injuryGiorgi Chakvetadze is suffering with a toe injury (Image: PA) Mattie Pollock and Pierre Dwomoh both face around a month on the sidelines with muscle injuries, while the game will also come too soon for Caleb Wiley, who is recovering from a back problem.
Kevin Keben and James Abankwah are the likely starters at centre-back in Pollock's absence, with just Manchester City loanee Max Alleyne – who signed on Friday – available as an alternative senior option.
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Pezzolano said: "We are definitely going to miss Mattie because he's a very important player and a great professional.
"He brings a lot of energy and a great work ethic so he's definitely going to be missed – but at the same time it's a great opportunity for the players that we do have to grow and fill that position.
"It's a message for everyone that we need them all to be ready.
"Max will need time, mainly to get to know his team-mates. He brings many good things, we feel he can help us in different positions and he's a very smart guy so he's going to pick it up quickly."
Max Alleyne has signed on loan from Manchester CityMax Alleyne has signed on loan from Manchester City (Image: Alan Cozzi/Watford FC) Edo Kayembe does return to the squad for the trip to The Valley, while Nathan Baxter has recovered from the knock that kept him out of the last two pre-season friendlies.
Of the players to have featured less in pre-season, Nestory Irankunda and Vivaldo Semedo are ready to go, while Othmane Maamma needs longer to reach a necessary physical condition.
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Pezzolano said: "Irankunda and Semedo and are ready to compete, they are in very good shape.
"Maamma arrived at the club in a physical condition that we think wasn't ideal so he has some extra work to do.
"Maybe it will take him a bit longer to be 100% ready."