The striker has been struggling with a groin injury and illness, although the interim Manchester United manager is keen to include him as the season draws to a close
The 28-year-old missed Saturday's 1-0 defeat to Sunderland at Old Trafford after suffering from a stomach bug and groin injury.
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"I hope he will play again this season, we will keep monitoring him and see how he is for Tuesday. Hopefully he will be back," said Giggs in his post-match interview after Saturday's defeat.
Ahead of the clash with the FA Cup finalists, Giggs highlighted the abilities of soon-to-depart Nemanja Vidic, whose eight-year stay at the club will come to an end this summer after agreeing to join Inter.
Giggs has hailed the 32-year-old as the best defender he has played with and admits the Serbian's absence will be difficult to fill next season.
He added: "Vida has been a brilliant player over the years, he is probably the greatest defender I have ever played with and I have played with some good ones.
"He is right up there, he is a brilliant player and obviously will be sorely missed."