United have been heavily linked with both players and Giggs believes Solskjaer should be given the necessary funds to sign Sancho and Grealish.
Speaking on the Webby and O'Neill Youtube channel, Giggs said: "Two good players. I think the thing with Grealish is he's obviously used to the Premier League and doesn't need to adapt to it so that's good.
"For me from the outside, it looks like he's got the mentality to come to this place and not bother him. Certain players can get overawed.
"Also, the good thing this year is he's got 10 goals and got into double figures so that would be one question mark I would have had with him: does he score enough goals? To get to double figures with no penalties for Villa is impressive.
"Sancho is quick, direct but also an intelligent player. What I like about him is when he gets into those areas with the final ball, he doesn't panic.
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"A lot of quick wide players sometimes do but he picks out the right pass. He's someone who can counter-attack if we're going to play that but also if a team are going to sit back, he can beat players and make things happen.
"They are two signings that may be available and if we're able to get them, I would go and get them."
United are in a much stronger negotiating position after securing a spot in next season's Champions League by finishing third.
That did seem unlikely earlier in the season but after Bruno Fernandes joined from Sporting Lisbon in January, they went on a 14 game unbeaten run in the Premier League and leapfrogged both Chelsea and Leicester City.
The lure of being able to play in Europe's elite competition will certainly appeal to potential new signings like Sancho and Grealish.