The wealthy Russian club's new boss Luciano Spalletti is determined to land an imposing centre-forward and is said to be a huge admirer of the 6ft 7in England star.
Zenit are keen on a move for Roman Pavlyuchenko but will look at other targets if the Russia international's price tag is much above £10million.
Tall order: Striker Crouch (front) is wanted by the rich Russians
However, their attention will stay at White Hart Lane, according to reports in Russia, with Zenit prepared to offer Crouch double his wages and the lure of Champions League football in a bid to pull off the unlikely switch.
Spalletti has inherited a squad desperately short of strikers but has been assured by club owners and energy giants Gazprom that he has the funds to add players.
Zenit look set to fail in a bid to sign Goran Pandev on a free. The Macedonia striker is set for Inter Milan after having his Lazio deal torn up.
Fiorentina's former Chelsea star Adrian Mutu has been linked as another candidate as the club try to make up for the loss of Andrey Arshavin, Pavel Pogrebnyak and Alejandro Dominguez over the last year.
Turkey international Fatih Tekke is also set to leave the club, who will play in Europe's premier competition next season after clinching third place in the Russian Premier League.
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