Robson has only just signed Speed from Bolton on loan and has no plans to part with the 38-year-old.
"That is a total non-starter as far as I'm concerned," Robson told the Yorkshire Post. "He is doing a really good job with us, no one has approached me."
Reports suggest McAllister could move for former Bolton boss Sammy Lee, who left the Trotters last October after just 11 games in charge.