The North Londoners currently have Igor Tudor in interim charge, but the Croatian has secured just one victory since his appointment in what has been a dire spell so far.
Spurs currently sit 17th in the Premier League and are just one point ahead of rivals West Ham in the relegation zone as fans worry that the side will drop to the Championship.
Following a 3-0 home defeat by fellow strugglers Nottingham Forest on Sunday, reports suggest Tudor could depart before club football returns.
Speaking to Jackpot City Casino, Keller says Spurs could convince one familiar face to return.
“Will Pochettino leave his role as USMNT manager? I definitely see him quitting after the World Cup. With Tottenham Hotspur, the problem, I think, is if they could entice Pochettino to quit the World Cup right now, and I could see that happening.
“I don't think they can continue down the path right now without hiring somebody and have the unthinkable happen.
“Timing is so important, I think if Spurs could get a couple of wins in the next couple of matches, obviously the Forest match what a disaster. Then you think hold off, wait until after the World Cup and then have conversations. I think Spurs need to make a real serious move right now or the unthinkable is possible.”
Many supporters would welcome Pochettino back with open arms but it is unlikely that he will leave before the World Cup to save the club from dropping down a division which may see the Argentine boss avoid returning.