The reigning champions have slumped to seventh in the table and look highly unlikely to qualify for Europe following a 1-0 defeat at Old Trafford to relegation-threatened Sunderland last weekend.
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"I have seen enough from this position to convince me that the next manager will be inheriting a squad capable of winning honours," he said in his programme notes ahead of the visit of Hull City on Tuesday.
"I don't buy into the theory that this club needs to bring in lots of new players and sell off a lot of the current squad.
"We have always strengthened here at United, in times of success as much as in times of rebuilding, and I am sure we will be doing business in the next transfer window, but a few carefully chosen recruits will bring the best out of the existing squad.
"We saw as recently as our win over Norwich that the players are capable of overrunning opponents, while the sheer number of winner's medals shared between the players in the dressing room speaks for itself.
"This is a club and a squad accustomed to winning, and every single member of the playing staff and coaching staff recognises that this season has fallen well short of the standards we have set."
Giggs, himself, has not yet ruled out continuing his playing career into the 2014-15 campaign, despite hinting on the contrary recently.
The 40-year-old admitted that he has not yet made up his mind, with a meeting with the new manager set to decide his future.
"When this season has finished, I will have to seriously consider what I'm going to do in terms of my own career.
"There have been times when I have felt that it wouldn't be right for me to play on next year, but then after other games - like the win over Olympiacos - I have had the urge to keep going.
"I have honestly not made my mind up either way, and there are a lot of things to consider - not least, of course, discussing the matter with the new manager here at Old Trafford."