A right-sided central defender has been Pep Guardiola's priority since City failed to replace former captain Vincent Kompany when he left the club nearly 18 months ago.
Goal understands that City are now ready to make a move for Portuguese international Dias, who could cost around €55 million (£50m/$64m).
Dias, 23, has been watched by club scouts for several seasons after three strong campaigns with Benfica and being part of Portugal's 2018 World Cup squad.
And the club is trying to get a deal for a new defender done before the transfer window closes on October 5.
Former Porto defender Otamendi could also be used as a makeweight in the deal with the Argentinian surplus to requirements at the Premier League club.
City have already signed Dutch international defender Nathan Ake earlier in the transfer window in a €44m (£40m) deal from Bournemouth.
Uncertainty also surrounds the future of young Spanish defender Eric Garcia, who is the final year of his contract and has turned down a new deal. Barcelona are preparing a bid to take the former La Masia player back to Camp Nou.
City struggled without the experience of Kompany last season and were forced to switch veteran Fernandinho back into the role from the centre of midfield.
The Brazilian started the opening day of the season back in his familiar role with John Stones partnering Ake in the heart of the defence.
Any new signing could be in consideration for City's Premier League clash with Leeds next weekend.
Guardiola is already short of options and says he has only 13 players available for Sunday's visit of Leicester City. But he is boosted by the return of Aymeric Laporte, who is available after testing positive for Covid-19.