The 40-year-old played the full 90 minutes on Wednesday night as United beat Olympiakos 3-0 to progress to the Champions League quarter-finals.
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But when quizzed about the possibility of taking over from the Scot after the game, Giggs insisted he is focusing on his playing career.
"I don't know anything about that,” he replied when asked by Sky Italia. “As you can see tonight I enjoy playing my football, and want to continue playing my football.
"This season wasn't what we expected. We need to play better, like we did tonight."
Giggs also hopes the victory over the Greek champions could turn around United's season.
"It's a good night for us,” he added. “Three days ago we lost here to Liverpool. We scored three and stopped Olympiakos scoring.
“We hope this can turn around our season.”