Mauricio Pochettino’s side have been drawn against Premier League rivals in the quarter-finals of Europe’s elite club competition.
The first leg of that contest is due to be staged at the newly-opened Tottenham Hotspur Stadium on Tuesday.
Home advantage could work in Spurs’ favour, having started life in the new stadium with a 2-0 win over Crystal Palace; but they face the toughest of tests against quadruple-chasing City.
Former Spurs boss Sherwood feels that Pochettino’s troops could not have been handed a tougher draw, with Pep Guardiola’s Blues currently the strongest side on the continent.
He told BT Sport: “On their day, we know Tottenham can beat anyone. They are going to need to have their day.
“Manchester City, for me, are the best team in Europe at the moment.
“If they are on song and they get everything going their way, they will win the game and the tie and go through to the semi-final.
“Tottenham have to believe, and I think they will.
“In their new stadium, they have got three points there in the league and got that out of the way.
“The fans will be up for it. It’s a massive occasion, one of the biggest games in the recent history of Tottenham.
“I give them a chance, but it’s an outside chance.”
Spurs have already come unstuck against City on home soil once this season, back in October.
That contest was, however, staged at Wembley Stadium, with an early effort from Riyad Mahrez settling the tie.
Tottenham are going to get plenty of practice when it comes to exacting revenge, with three of their next four games coming against City.
Spurs' Champions League quarter-final ties fall either side of a meeting with Huddersfield, with the second leg then followed by an immediate return to the Etihad Stadium for the teams' Premier League clash.