Falcao is instead likely to move to Chelsea and Mancini, with his new management structure in place, wants the club to show their intent by attempting to prise Suárez away from Anfield.
Having recently secured the Uruguayan international on a new contract, Liverpool are in a position to put off bidders with a price tag well in excess of the club record £50million they received for Fernando Torres two years ago.
Even a bid that would shatter the British transfer record would not be welcomed by the Anfield hierarchy who recognise the importance of Suárez to Brendan Rodgers' rebuilding plans.
The 25-year-old has scored 11 goals in 16 games in all competitions for his club this season, including eight in the Premier League, and despite his chequered disciplinary record, his absence would represent a huge blow to the club's hopes of regaining their former status.
Suárez himself has shown no inclination for giving up on inspiring the Merseyside club back into the top four and Liverpool will be confident any January move is doomed to fail. Indeed, the club's priority remains trying to recruit new players when the transfer window reopens.
Rodgers, for his part, reiterated Liverpool's hard-line stance last weekend. "At this moment in time I'm safe in the knowledge that Luis had the chance to go in the summer," he said. "There was probably no better time for him to do that with a new manager coming in.
"He could have had an excuse to go, but having spoken to him at length he committed to staying here. He gave us that opportunity to see how it was going to work. It's up to us as a club to add players that can help support him and move us on."
Mancini's determination to test the resolve of Liverpool and their talisman perhaps reveals more about his frustration with strikers Mario Balotelli and Edin Dzeko, both of whom appear available for the right price.
Balotelli was left out of the squad to face Spurs last weekend and has been at the centre of several disciplinary problems. He has also failed to score a Premier League goal all season.
In contrast, Dzeko is City's leading goalscorer in the league with six goals, but he appears to have lost the confidence of his manager, who has started him just three times.
The Bosnia-Herzegovina international has aired his frustrations at being used mainly from the substitutes' bench and it would be no great surprise for him to be moved on before the start of next season.
With even the normally reliable Argentine duo of Carlos Tevez and Sergio Agüero struggling for form, City and their new director of football, Txiki Begiristain, are prepared to enter the market in the new year.
But directors have made it known to Mancini they must embrace new Financial Fair Play rules, making astronomical transfer fees less likely in future.