The report claims that the Blues have been keeping tabs on the former Valencia man over the first half of the season and are considering bolstering the midfield with the addition of the Turkish international.
Blues boss Guus Hiddink knows Topal well having coached him during his time in charge of the Turkish national team.
Chelsea could end up signing Topal as a free-agent should they decide to wait until the summer as the 29-year-old has just six-months remaining on his contract.
The experienced midfielder has made 29 appearances in all competitions for the Yellow Canaries this season establishing himself as a first-team regular.
Topal enjoyed two-seasons at Valencia after joining from Galatasaray in 2010 and played for two-seasons at the La Liga side.
The defensive midfielder is nicknamed ‘spiderman’ due to being double footed and is a regular in the national team setup.