Spurs want to enlarge their stadium by 16,000 to a capacity of 52,000 and are looking for an alternative home for two seasons while the £300million work is carried out.
"We did have a meeting with Tottenham but really they were only asking us what we thought of the possibility of a ground-share," said West Ham chief executive Scott Duxbury.
"We said we would go away and think about it but that is as far as it has got."
It is reported that Spurs are also looking at the possibility of playing some of their matches at Wembley Stadium.
The plan would be for the club to stage most of their home matches at Upton Park, moving to Wembley for selected big games such as the derby against Arsenal.