The club are set to move away from Upton Park, after holding off a lengthy legal challenge from both Tottenham and Leyton Orient.
Spurs, meanwhile, have plans to build a new ground, close to their current White Hart Lane home, although their preparations suffered a blow earlier this month.
The club announced it was unlikely that the arena would be ready for the 2017-18 season as originally intended, because of a High Court challenge to their plans.
With Tottenham potentially homeless during the intervening period, it was put to West Ham vice-chair Karren Brady at a media conference on Tuesday that another club could share the Olympic Stadium.
Brady did not mention Tottenham specifically, but with Orient's legal challenge having come to an end, her response looked to be one directed at Spurs.
"In reality they probably could," she said. "But only with our permission, and no-one has asked us for permission.
"And even if they had, we would probably say 'no', depending on who it is - if you catch my drift.
"We are the anchor tenant for the winter matches and nothing else can happen in that time without our permission and our football matches take priority over everything else.
"If there are events at the stadium we have approved we do not see any of the revenue from that."
