The 24-year-old has not featured so far his season and has been deemed surplus to requirements as Brighton have gone out and recruited well this summer.
Everton have made five signings this summer but there has been movement on any signings on deadline day so far.
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.”
Alzate played just 661 minutes last season and he has only played 51 times for the Seagulls since making his debut in 2019.
He spent most of last season on loan in Belgium at Standard Liege where he managed two goals and five assists in 24 league games.
His current deal expires next summer and he is valued around £3.4m and would certainly be a cheap acquisition if Everton were to move for him - as it stands, there’s been no official bid.
Alex Crook of TalkSport revealed a few days ago that Everton were interested in a potential move, but with just hours left of the window, there has been no move. Wolves are also reported to be keen.
Everton have made five signing during the summer window so far, with Arnaut Danjuma, Beto, Ashley Young, Jack Harrison and Youssef Chermiti all arriving, but the general consensus amongst fans on social media is that more signings are needed.