Portsmouth chairman Milan Mandaric says talks will soon begin on a new contract for boss Harry Redknapp.
Redknapp will be offered a new deal - if Pompey stave off relegation or not - - after winning over the fans who were sceptical about his return.
Mandaric told BBC Sport: "I was disappointed with some fans' attitude when Harry came back from Southampton.
"I appreciate it was an emotional time but I'm happy they're coming back round with the decision to bring him back."
Redknapp was only given a contract until the end of the season upon his controversial return to Fratton Park from neighbours Southampton.
Mandaric stressed he and co-owner Alexandre Gaydamak were keen not to distract Redknapp's attention from winning Pompey's fight against relegation.
"If the worse should happen, we would want Harry to be the man to get us back into the Premiership"
Portsmouth are currently second from bottom in the Premiership and Mandaric added: "At the moment all our concentration is on every game between now and the end of the season.
"Harry understands that but he also knows that we want him to stay - so he can do his job with that knowledge.
"So there is no rush but at some time between now and the end of the season we will sit down and start to talk."
Mandaric insisted: "We are not thinking about relegation and we obviously think we can stay in this division.
"But if the worse should happen, we would want Harry to be the man to get us back into the Premiership."
Redknapp's stock among supporters has risen following three successive wins, which have pulled Pompey back from the brink.
Fans who were angry at Redknapp's defection to Southampton in November 2004 initially refused to acknowledge his return.
But following Pompey's 3-1 win at Fulham on Saturday, supporters chanted Redknapp's name for the first time since he came back to the club.
Mandaric said: "I think the vast majority of supporters were with my decision to bring Harry back, I think it was only a minority that were against it.
"But I'm happy that they have come around to my way of thinking."
Meanwhile, Pompey's survival hopes have been dealt a blow because of a knee injury to striker Benjani Mwaruwari.
Boss Harry Redknapp told BBC Radio Solent the club record £4.4m capture from Auxerre may have a slight cartilage tear.
And Pompey midfielder Pedro Mendes fears he will be overlooked by Portugal coach Felipe Luis Scolari for this summer's World Cup finals in Germany.
Mendes told BBC Radio Solent: "I've not even been involved in friendly games, so I don't have any hope of going."