Golovkin will defend his WBA, WBC and IBF middleweight titles against Alvarez in Las Vegas tonight in a bout scheduled to start at 4am UK time.
If he wins, a bout against Saunders would see the first unification since Bernard Hopkins in 2004 after the Brit successfully defended his WBO strap in London.
But Warren has promised that Saunders will be straight back into training camp for a bout in December and that Golovkin is the clear target for that fight.
“Hopefully, if Golovkin wins and he doesn’t get banged up, that could be a Golovkin fight in December,” Warren said.
“If Alvarez wins, then that would be next year. Even if Golovkin loses, that’s still a great fight. They are good fighters.
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“We had to get this fight out of the way. There was a lot of pressure on him tonight and he puts pressure on himself.
“He came through, he did it and that’s what is important.”
On his last outing, a win over Artur Akavov in Glasgow, Saunders admitted he was far from his best.
And while this was an improved performance, the ring-rust caused by nine months out was clear and he was only allowed to dictate the fight by the inactivity of Monroe.
But Warren was delighted that his man, who has moved to Dom Ingle’s gym and claims to have rediscovered his “hunger” for boxing at the Sheffield base, got the job done by any means possible.
“I want him to be busy. He’s had a real bad year last year with fighters pulling out and so forth,” Warren added.
“There is ring-rust there but he’s got that out of his system and more importantly, he’s got 12 rounds under his belt.
“That for him is in the bank. We’ve got to move on to December and get him out again.”