The Spain international is believed to be the more achievable target for the defending Premier League champions, but City director football Txiki Begiristain is thought to have made both players transfer priorities this summer.
The 23-year-old Reus was watched by City while still at Borussia Monchengladbach last season, but the Germany international eventually opted to join Bundesliga champions Dortmund. His deal with Jurgen Klopp's side doesn't expire until 2017, and he's thought to be valued at close to £30m by the German side.
Navas has a £35m buyout clause in his Sevilla contract, and while City have the funds to match such a fee, the La Liga club could be willing to accept around half that sum considering the winger's contract runs out in 2015.
The Spain international was part of the World Cup winning squad of 2010, and the Euro 2012-winning set-up in Ukraine and Poland last summer.
But the 27-year-old is thought to have homesickness problems when travelling away for long periods, and he may not be open to a move to Manchester.
The report claims the two internationals are the latest additions to a lengthy transfer wishlist being put together by Begiristain.
And new wide-players are the main priority for Mancini's side. So far this season City have been forced to rely on their full-backs to provide their width, as Samir Nasri and David Silva often tuck-in.
As well as Reus and Navas, City reportedly have their eye on Derby teenage midfielder Will Hughes, Napoli striker Edinson Cavani and Celtic midfielder Victor Wanyama.
But to help finance their summer moves, Mancini is reportedly willing to offload a number of first-team players, including Edin Dzeko, Samir Nasri and Scott Sinclair.