The spectacularly successful 41-year-old coach prefers to renew his deal with the Spanish and European champions on an annual basis and as the season has slipped by mutterings about the possibility of him leaving in June have grown in volume.
Barcelona President Sandro Rosell is desperate to persuade Guardiola, who has led the Catalan club to 13 trophies since taking over in 2008, to agree an extension, although he has so far refrained from putting too much public pressure on the former Barca and Spain midfielder.
"The sooner the better," Rosell told reporters on Tuesday when quizzed about the issue.
"That would always be a massive boost, it would be great," he added.
Real, who play at city rivals Getafe on Saturday, have a seven-point lead over Barca with just over half the season played and are fiercely determined to end their arch-rivals' domestic and European domination.
Having knocked Real out of the King's Cup last week, Guardiola refuses to give up on the league title, although he admits Barca are "almost at the point of no return" after Saturday's 0-0 draw at Villarreal.
They clung on to draw 2-2 with Mourinho's side in their cup quarter-final second leg, which sent them through 4-3 on aggregate, and were held to a 1-1 stalemate at Valencia in Wednesday's cup semi-final first leg.
It was the first time since March 2009 Guardiola's side had been restricted to three consecutive draws.
"A lot of people believe the league is already lost, but they will not convince me," he told a news conference on Tuesday.
"Let me believe that we can win again and if we cannot we'll congratulate our opponents," he added.
"We've done well for a long, long, long time, and you don't know how hard that is.
"The players must put in the effort to continue. They will regret it if they don't. We cannot give up yet."
Levante, Valencia's city neighbours and the season's surprise packages, are five points further back in fourth and host troubled Racing Santander on Saturday.
