City have yet to concede a goal in three games under Mancini but defensive frailties were their undoing under sacked Mark Hughes - and Vieira is seen as another vital piece in the jigsaw.
Former Inter coach Mancini knows the Frenchman well and has offered him a £140,000-a-week deal to join City on loan for the rest of the season, says The Sun.
Vieira, 33, is due in Manchester today after saying farewell to his Inter team-mates last night.
He is eager to relaunch his career ahead of the World Cup this summer after failing to hold down a regular place in Jose Mourinho's team this season.
There is also the added incentive of a further year's contract with City if all goes well.