Warburton, who is on the mend after sustaining a knee injury in April, will captain his second Lions squad and Gatland said that the Welshman must focus on his fitness.
"It would be ideal for us if he didn't play for the Blues," Gatland told British media.
"Sam thinks he is ok at the moment. The plan is that he will stay with us and do some hard conditioning work with contact as well."
Gatland is wary of teams in New Zealand that would like to upset the Lions and gain recognition.
"The opposition teams will relish a Lions scalp and my challenge is to communicate that to the squad... they will see it as a chance to make a name for themselves, do something special, create a bit of history," Gatland said.
Gatland also said that he had prepared a list of reserve players that could fill on for withdrawals and injuries but refused to release it to the public.
"In our minds we have players who we will notify for standby, but we also have to be flexible," Gatland added.
"We won't publish it in case we change our minds. We don't want to back ourselves into a corner."
The Lions begin their New Zealand tour against the Provincial Barbarians at Toll Stadium in Whangarei on June 3.
(Reporting by Aditi Prakash in Bengaluru; Editing by Amlan Chakraborty)
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