The Sun says the relegated Blades plan to offer 8m for Patterson.
The keeper, 24, has a deal to 2028 with Sunderland.
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Liverpool have also been scouting Patterson this season. The Premier League giants may be in the market for a no 2 goalkeeper in the off-season.
As the Reds consider the possibility of allowing Caoimhin Kelleher to leave, Patterson may take his place.