HITC Sport is reporting that the Whites boss wants Nick Powell while The Sun is of the belief that Ashley Fletcher is on the radar of the West Yorkshire outfit.
Monk is determined to strengthen the squad he has inherited at Elland Road and is hoping to push for promotion in his debut season.
The 22-year-old is out of contract on June 30 and could be open to joining Leeds but there is expected competition from the likes of Nottingham Forest, Aston Villa, Norwich City and Wigan Athletic - the latter where he starred on loan in 2013/14.
20-year-old striker Fletcher did well while with Barnsley last term, helping the Tykes achieve promotion to the Championship, and is also the radar of Leeds who could offer him a permanent deal.
However, United may want to hold onto the talent and could send him out on loan to Oakwell again after developing so well in South Yorkshire last term.