The idea of returning Dzerzhinsky to Lubyanka Sqaure was floated on various occassion (and for various purposes). In 2021, the city of Moscow even organised an online vote for residents to decide whose statue should be placed on the square in front of the FSB building: returning the toppled Dzerzhinsky, or erecting a statue of Aleksandr Nevsky instead. But the vote was cancelled mid-way.
The political usage of the memory of Nevsky, by the way, is not without its issues either as it has been used by a tandem of the Russian Orthodox Church and the Russian Ministry of Foreign Affairs to promote a conservative idea of a 'Russian world' (see also the chapter linked here)
Attempts to return Dzerzhinsky into the public domain fit into a larger trend of normalising - or even glorifying - state repression. Putin's long-standing promotion of Stolypin carries similar connotations (here's Stolypin spotted by FBK on Putin's yacht in one of their most recent investigations).
Favoured by Putin himself, Stolypin got his statue in Moscow already in 2012 (though the statue was not placed on Lubyanka square to fill the empty spot where the toppled Dzerzhinsky used to stand, as Nikita Mikhalkov had proposed as early as 2001 - as I outline in the chapter linked below).