Spurs are trying to sign Manchester City's former Arsenal striker on loan after their problems in front of goal, which cost them a place in the Premier League's top four last season.
Redknapp's team had no such scoring problems on Thursday night, as they embarrassed Hearts 5-0 at Tynecastle in the Europa League play-offs.
But with Robbie Keane having joined LA Galaxy in midweek, there is room for another forward and Redknapp is optimistic Adebayor will soon arrive.
Tottenham chairman Daniel Levy is in discussions with City regarding the Togo hitman, who has an excellent record against Spurs and scored twice against the Londoners while on loan at Real Madrid last season.
Redknapp said when asked about the Adebayor deal after the victory over Hearts: "I honestly don't know. The chairman deals with that.
"I've never spoken to the player or Manchester City or anybody there.
"He (Levy) will be dealing with that at boardroom level.
"It seems to have been progressing along and it seems like it probably will happen, but I'm not 100 per cent sure."