Ferguson had accused Ferdinand of embarrassing him after the player refused to wear a 'Kick It Out' anti-racism T-shirt in the warm-up prior to the 4-2 home win over Stoke City on Saturday.
The long-serving Scot had said prior to the game that all his players would wear the T-shirts, stressing his view that a united front was the best approach.
Ferdinand's younger brother, Queens Park Rangers defender Anton, was the subject of racist abuse from John Terry last year, for which the Chelsea captain is currently serving a four-match suspension.
After Saturday's game, the Scot claimed Ferdinand had let the club down and would be "dealt with".
But any tension between the two appeared to have thawed by Monday, with Ferguson hinting that the 33-year-old player could even be offered a new contract when his current deal expires at the end of the season.
"I think Rio could play for another two or three years," said Ferguson at a press conference in Manchester ahead of United's Champions League game with Portuguese side Braga at Old Trafford on Tuesday.
"He's not as quick as he was but that's not a problem for me. There's no reason why he can't stay on for another year."
On his disagreement with Ferdinand, Ferguson added: "The issue is pretty simple. I spoke to Rio. I think there was a communication problem. I think he felt I should have spoken to him on Friday.
"I didn't anticipate that there would be any problem in the dressing room as far as the T-shirt was concerned.
"My advice to him is that I always think the union is stronger than any individual and it is important he airs his grievances to the right people, through the PFA (Professional Footballers' Association) or the FA (Football Association).
"It has been a communication problem rather than anything else. Obviously as the manager of the club, when you lay down policy you don't want to see it being ignored, and that's where my anger came from on Saturday.
"We have resolved the problem. There are no ongoing problems and we've moved on. That's the end of the matter. We will carry on with the football side of it."
With United, second in the Premier League, away to leaders Chelsea on Sunday, Ferguson revealed that Ferdinand will be left out of his starting line-up for the visit of Braga.
But he was at pains to stress that his decision was motivated by the need for Ferdinand to be rested ahead of the trip to London at the weekend, rather than as a result of any disciplinary measures.
French defender Patrice Evra will also not start against Braga, who are third in Group H after one win and one defeat from two games.
Braga are third in the Portuguese top flight and Ferguson is anticipating a difficult evening for his side, who overcame Galatasaray and CRF-Cluj 1-0 and 2-1 respectively in their opening two group matches.
"Braga, to my mind, are better away from home and showed that by beating Galatasaray," said Ferguson.
"It's not easy going to Turkey. In the modern European game, counter-attack is the issue, so tomorrow hopefully we can deal with that issue."
I've made peace with Rio Ferdinand, says Alex Ferguson
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