Louis van Gaal, who is about to lead the Netherlands at the upcoming 2014 FIFA World Cup Brazil™, remains the hot favourite to be that man. But after Giggs's second game as temporary manager ended in a humbling 1-0 defeat by Sunderland at Old Trafford on Saturday - United's seventh home reverse in the league this season - the Welsh winger admitted his side have fallen dramatically short of the necessary standards.
"You need to improve all the time," said Giggs, English football's most-decorated player. "Consistency obviously wins you trophies and titles and we were nowhere near that this season. That's obviously a problem. It's a problem that needs to be solved next year. I still believe there is quality here but we obviously didn't show it today (Saturday).
"We've not shown it consistently over the season. Until we do that, we will carry on having results like today and that's frustrating. I still believe there is quality in the dressing room. They showed that last week but didn't this week. Whether it be a lack of confidence or concentration I honestly don't know.
"We've shown it away from home, shown good form away from home, but it's been a problem at Old Trafford this year. In past seasons, there have been wave after wave of shots and saves, you could always see goals coming. This season, it just hasn't happened. I can't tell you anything about the next manager, I am just concentrating on the next game."
That next game comes on Tuesday when Hull visit Old Trafford with United keen not to record an eighth home defeat of the campaign - the seven suffered to date already representing the same total they suffered in the last four seasons, combined, of Sir Alex Ferguson's reign.
The last home game of this disappointing campaign will also be the final Old Trafford date for a number of players - such as veteran defenders Nemanja Vidic and Patrice Evra and possibly even Giggs himself if he cannot negotiate a role under the new management. "It's the last home game so we want a positive result," said Giggs. "[Vidic] has been a brilliant player over the years, probably the greatest defender I've played with and I've played with some good ones. He's a brilliant player and will be sorely missed."
Seb Larsson took advantage of some poor United defending to score the only goal of the game after half an hour but so impressive was Sunderland's performance they also struck the woodwork twice in the closing stages. Victory went a long way to assuring Sunderland of retaining their Premier League status, in a season that saw them reach the League Cup Final at Wembley where they lost to Manchester City.
More recently, victories at Chelsea and United, plus a league draw at City, have taken Sunderland to the brink of safety. "What we've done over the past four games is unique and special," said Sunderland manager Gus Poyet, whose team have also beaten relegated Cardiff, in that spell. "Apparently, every now and then miracles do happen. We're in a position now where if we win one of our two home games (against West Brom and Swansea) we are over the line.
"After we lost to Everton, we needed to win four games and had three at home and three away at very easy places - Manchester City, Chelsea, Old Trafford!," the former Uruguay midfielder joked. But you need to expect the unexpected from us and that's because of the players. We have more than ten players out of contract but they have not been thinking of next year or their next club. They have been fighting for the club, fighting for the fans because they don't want to accept it and go down. That makes me very proud."