Luiz, 23, has emerged as a target for the big-spending Blues, although they have hit an impasse over his transfer fee as they refuse to meet the Portuguese side's £29.3 million valuation.
With the Brazil youth international comfortable at left or centre-back, his arrival would significantly boost Roberto Mancini's squad if a deal could be forced through.
According to O Jogo, though, City's pursuit is in vain. The player has set his heart on a switch to los Blancos or the Red Devils and would, for this summer at least, turn down any move to Eastlands as he awaits moves from higher up the food chain.
Benfica will be playing in the Champions League next season and have already lost star winger Angel di Maria to Madrid in a deal worth around £25 million.