Buckley who officially plays in the Bundaslegia for Dortmund has spent the last few weeks on trial with David Moyes Everton on their tour of America.
The 28 year old impressed whilst taking up the roles of Left-Wing and Center-Forward with the Toffees; though the Goodison Park manager is considering his options.
Meanwhile the Blades have decided to take the African on trial - and could table a bid soon.
"Delroy is training with Sheffield for a few days," his business manager Rob Moore told skysports.com.
"It might be an option for him, but Everton have still not made a decision.
"We will have to see how things progress this week."