The Super Lig side were the subject of speculation in the Turkish press this week, which suggested they were looking to bring in the experienced duo.
Cech has struggled for games this term in the Premier League, with Thibaut Courtois now established as Jose Mourinho's number one, while the reports also suggested Danny had visited Istanbul with a view to joining the club.
However, the club released a statement via their official website in which they described the rumours as "unfounded".
While Mourinho has spoken of his desire to keep the long-serving Cech at Stamford Bridge, the goalkeeper has previously hinted he may be ready to seek a new challenge.
Cech - a regular prior to this season following his move from Rennes in 2004 - has also been linked with a move to Chelsea's Premier League rivals Arsenal.
Danny captained Zenit to third in UEFA Champions League Group C this season, while they lead the Russian Premier League by five points from CSKA Moscow.
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