With his contract set to expire in June, the 35-year-old former England captain had appeared set to finish his 12-year career at the club after being used sparingly under recently sacked Scotsman Moyes.
"I'm going to continue playing," Ferdinand told British media. "Whether it's here, I don't know, but I hope so.
"I am sure that whoever is here, whoever is managing, the aim of this club is win trophies and championships and we have done that for 25 years. Long may that continue."
After winning last year's league title in Alex Ferguson's final year as coach, United plumbed new depths under former Everton manager Moyes, and will miss out on the next Champions League tournament, a once unthinkable prospect.
Interim coach Ryan Giggs took the reins with a 4-0 win over Norwich City on Saturday, their biggest home league victory of the season. The win kept them seventh on the table, six points behind Tottenham Hotspur.
Ferdinand was unable to explain the team's immediate improvement without Moyes in charge.
"The person who has the correct answer to that would be a genius," he said. "If we knew why, then I'm sure the change of manager wouldn't have happened. I've not looked at the league table for ages.
"We were saying it before the game. It's because you don't want to. It's embarrassing. You don't want to look at the league table and see where we are, but that's down to us as players.
"We take responsibility for that as much as anyone else. We are where we are and we have to take some responsibility for that.
"We are not shirkers and we are not people who don't take responsibility. I don't think you get to where we have got to in our careers without taking responsibility and this is no different."
Giggs has been backed to continue as United's full-time boss by Ferguson, but Dutch media have linked Louis van Gaal with the role once he finishes his World Cup commitments with Netherlands' national team in Brazil.