Morris was left out of the side that beat Gillingham 2-1 on Saturday, keeping them in bottom three but just one point difference between them and Nottingham Forest.
Lee Morris: Bramall Lane bound
"Sheffield United made a bid two weeks ago which was turned down, but they've made an improved offer and the clubs are close to an agreement," Burley explained.
"Lee is a Sheffield boy and he's interested if the clubs agree and I thought it was better that we left him out. On Monday or Tuesday, if everything is agreed, we will allow him to talk to United."