Adkins revealed last week that the Barnsley forward Kayode Odejayi was a target, before then having to admit that a deal was unlikely.
Now Gareth Taylor, the veteran Doncaster Rovers forward, as turned down a move to Glanford Park.
Taylor, 35, has not scored in 18 appearances for Rovers this season and was deemed surplus to requirements by their manager Sean O'Driscoll.
"I spoke to Gareth and, at this particular time, Gareth wants to stay," O'Driscoll told Rovers' official website.
"We would have been okay with Gareth going there for a month. But it's Gareth's prerogative and that's not a problem. That might change as things progress, but at this minute in time he is happy where he is."
United are in need of a forward to provide cover for the first choice pair of Paul Hayes and Gary Hooper.
Ben May is injured and Adkins has appeared reluctant to include Jonathan Forte or Peter Winn in squads.