Alzate has been linked with a late move to Goodison Park after being deemed surplus to requirements on the south coast by the Brighton boss.
When asked about the midfielder's future, De Zerbi said: “Unfortunately it is difficult to have more than two players in every position. I spoke this morning and last week with him. We will see in the next hour in the transfer market and then I can answer you.
"But if he stays, I will not forget him. We will play a lot of games and I think Alzate can become important during the season.”
The 24-year-old has made 51 appearances for the Albion, achieving cult hero status when he scored the winning goal in Brighton’s famous 1-0 win away at Liverpool in 2021.
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The emergence of players such as Yves Bissouma, Moises Caicedo and Alexis Mac Allister has limited the Columbian’s first team opportunities, leading to a season-long loan at Standard Liege last term.
Despite impressing whilst playing in Belguim, Alzate returned to pre-season training with the Seagulls this summer, having once again found himself low down in the midfield pecking order.
Alzate was not named in the Brighton squad for the West Ham or Wolves game and was an unused sub in the 4-1 win over Luton.
There is yet to be an official bid from Everton, with Wolves also said to be interested in signing Alzate.
The Midlands club are searching for a midfield replacement having sold Matheus Nunes to Manchester City for £42m.