According to The Daily Mail, the Russian champions are ready to step up their interest in the Portuguese international.
Nani has suffered a difficult start to the Premier League season. After a dismal performance in United's opening fixture against Everton, he was completely dropped from the next squad.
Sir Alex Ferguson also benched Wayne Rooney for a poor display against his former club, but Nani's omission could have greater consequences.
The emergence of Antonio Valencia as United's most influential right winger has put Nani under constant pressure across the past year. Ashley Young is often favoured on the left, meaning the performances of the former Sporting Lisbon player have come under increased scrutiny.
Nani has always been inconsistent. His entire United career can be defined by an inability to maintain world-class performances across a full season.
Last year, he scored eight goals and provided 10 assists to a United side that narrowly missed out on the Premier League crown. Unfortunately, this doesn't tell the whole story.
A player of Nani's caliber shouldn't frustrate as often as he does. If he jogs over to take a corner, United fans know it's going to hit the first defender. For someone who possesses such fierce shooting power, the ball has ended up in row Z of Old Trafford's Stretford End far too regularly.
Nobody can question Nani's influence over the past few years. He has played a major role in much of United's success. The problem is, United is built on the legend of wingers such as George Best, Ryan Giggs and Cristiano Ronaldo, making Nani's shortcomings far too obvious.
As Zenit mull over a deal, the Manchester Evening News suggest Nani could stay in the Premier League with a move to Spurs.
Andre Villas-Boas has money to spend after Luka Modric completed a £33 million transfer to Real Madrid, and it wouldn't be surprising if he offered his fellow countryman a route away from the Red Devils.
The transfer window remains open until 11pm (GMT) on August 31. If Zenit and Spurs want to land the player, expect progress to happen quickly.
Nani has the ability to play himself into a new contract at Old Trafford, but right now, his future is looking as hit and miss as his performances.