Woodburn was linked with moves to both Sheffield United and Villa this summer, with the Championship duo keen.
However, Klopp warned the £10,000-a-week striker (Daily Express) against making the switch to Villa.
The Liverpool manager reportedly felt that Woodburn could have struggled for game time at Steve Bruce’s side.
Villa did have Josh Onomah and Robert Snodgrass on loan last season, and played the pair both regularly.
However, with Villa lining up in 3-5-2 in pre-season, and still having the likes of Jonathan Kodjia and Scott Hogan at the club, Woodburn would have faced fierce competition for a place up-front at Villa Park.
The youngster’s task looks more straightforward at Sheffield United, and he could make the move to Bramall Lane in the coming days.