Gallagher has been underwhelming since his January arrival from Atletico Madrid.
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De Zerbi tried to sign him as Brighton manager when Gallagher was playing for Chelsea.
Ahead of today's debut at Sunderland, the Italian said: "For Gallagher it has not been easy.
"He left Chelsea after I don’t know how many seasons, went to Atletico Madrid, and now in Tottenham, in this moment for Tottenham.
"He was a leader in Chelsea, and now he has to adapt to a new club, to new teammates, to a new stadium, to a new everything.
"I have to help him to put as a target the Gallagher he was at Chelsea."