There is growing support inside the dressing room and from the club's vast fan base for Giggs to be handed the Manchester United job on a full-time basis.
However, United are set to appoint Louis van Gaal instead as the Holland coach has far more experience than the Welshman, who is yet to complete his UEFA Pro Licence exams.
But Giggs had nothing but warm words for Van Gaal when asked about his potential successor on Friday morning.
"He has a brilliant reputation," the United interim boss said.
"He is a successful manager in different countries. Obviously he has taken Holland to the World Cup. He has a fantastic pedigree."
What role Giggs plays under Van Gaal remains to be seen. A number of options remain open for Giggs, who started his four-match spell in charge with a 4-0 win over Norwich last weekend.
Giggs could coach under Van Gaal, he could play for the Dutchman or he may depart for pastures new after 24 years at Old Trafford.
The midfielder says he will not decide his future until the end of the season.
"My concentration is on the remaining three games and then I will see what happens at the end of the season," Giggs said.
"I have got to decide if I want to play or not, so there is no point thinking if I want to be an assistant or if I want to be a manager somewhere else.
"There are so many things to think about, but that's in the future.
"I honestly don't know (what I will do)."
When the 75,000 fans inside Old Trafford stood to applaud Giggs as he strolled down the touchline in his club suit last Saturday, it was like a scene out of a Hollywood film.
If Giggs is to say goodbye to United this summer, there are only two more chances for him to run out on to the pitch at Old Trafford.
Giggs hinted that he will not ditch his suit and slip on the United kit for Saturday's match against Sunderland and there is a possibility that he will not turn out in the final home match of the season against Hull three days later.
He said: "As footballers, we are pretty superstitious so (I will keep) my suit on (for the Sunderland game), unless I am playing, of course!"
"I am still training and doing bits and pieces so I am still in the frame for playing the remaining games or being involved.
"My main priority is winning the games. Does me playing give us the best chance? We will see.
"I might not get back in the team."
Not even the prospect of scoring in his 21st consecutive Premier League season would affect Giggs' judgement on the matter.
"It would be nice (to score) but I am not too bothered about that," Giggs said.
Although he is not likely to be at the helm next year, Giggs has held discussions with executive vice-chairman Ed Woodward regarding future plans for the club.
The pair have discussed United's summer tour of the United States, the possibility of Europa League qualification, and the futures of the squad members who are out of contract.
Nemanja Vidic has already confirmed he will leave for Inter Milan, but Giggs has been pressing for United to offer new deals to experienced defenders Rio Ferdinand and Patrice Evra.
"I do believe they still have a part to play (next year)," Giggs said.
"Both their contracts are up but they have both given massive service to the club.
"They are both fit and they both looked good last week. I don't see why not.
"Decisions on a lot of players were made four or five weeks ago. It is just a couple that are a bit up in the air. I have just given my point of view, then we will make a decision.
"The decision will be down to everyone - Rio, Patrice, Ed and whoever is the manager next year.
"It is a group discussion but I still think they have a lot to offer. They have been great players and they remain assets to a club like Manchester United."
After such a disastrous season under David Moyes, who left the club in seventh, Giggs concedes the club need to make new additions to the squad in the summer.
"It has not been a great season this year. It is important we get the right players in and we improve on this season," he said.
Giggs will consider resting Wayne Rooney for Saturday's visit of Sunderland as the striker is struggling with a combination of a groin injury and illness.
That could open the door for fit-again Robin van Persie, who has been out for over six weeks with a knee problem.
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