Manchester City's Shaleum Logan, Gregory Vignal of Birmingham and Arsenal's Kerrea Gilbert have all been training with the Blades and appeared in Saturday's 2-0 friendly win over Rotherham.
Assistant boss Sam Ellis said: "We know we need extra cover in case of injury and suspensions and that is what we are aiming for.
"We won't be signing Vignol, Gilbert or Logan and the search goes on. We are endeavouring to find the right additions and there will be more to look at next week.
"There are no definite names to announce right now but there will be on Monday because they will feature at Notts County on Tuesday night."