Stewart has completed a loan switch from Hull City while Jimmy Kebe is also in talks with the Whites over a loan move from Premier League side Crystal Palace.
Phil Hay in the YEP reports that 24-four-year-old Barnes could be next on United’s list of targets.
Burnley are competing for his signature and have had a bid accepted by Brighton but United also hope to land a forward who has been heavily involved in Albion’s season but is out of contract in the summer.
Barnes has played 24 times for Brighton this term, scoring six goals.
Winger Stewart, 22, has joined on a 93-day loan but has signed a three-year deal which takes effect in the summer.