Turnbull, the Motherwell midfielder, returned to Fir Park last week when a medical examination revealed a problem with his knee. The teenager had rejected a move to Norwich City, who were promoted to the Premier League alongside United last term, in favour of Neil Lennon's side. But with Celtic now refusing to process the deal, there have been suggestions Lennon's employers could use the money they have saved to return with an improved offer for Baldock, despite United's refusal to entertain the prospect of selling him earlier this month.
Although any further enquiry is guaranteed to receive the same response - "We told them (Celtic) 'no' and not to waste their time by coming back," a source at Bramall Lane told The Star when the Glaswegian's interest was first revealed - it would prove an irritation for Wilder as his squad begin their preparations for the new campaign.
Satisfied Celtic's initial interest was encouraged by an intermediary rather than the player or his representative, United have received reassurances that Baldock, who is understood to have recently changed agent - has no intention of leaving Bramall Lane.Indeed, the likelihood is he will be invited to sign an extended contract before his present agreement expires next summer.
Baldock, previously of MK Dons, made nearly 30 appearances as United returned to the top-flight for the first time since 2007, finishing five points behind City and six ahead of third-placed Leeds.
Turnbull, aged 19, had appeared destined for Carrow Road before performing a u-turn and accepting Celtic's offer instead. The midfielder's mind is believed to have been swayed by City's plan to loan him to a Championship club for 12 months before recalling him to Norfolk.
Lennon wants to bolster his defensive options after allowing Mikael Lustig and Cristian Gamboa to depart.
But he insists he is unaware of any interest from United in Scott Sinclair, whose future in Scotland was the subject of intense speculation last month.
"There's nothing in that one that I'm aware of,” Lennon told newspapers north of the border. "Scott had another decent year in terms of his goal return and he has looked after himself really well over the summer and come back in really good condition. We are not looking to sell but there might be interest in him. It just hasn't manifested himself."
"I think Scott is happy here," Lennon added. "The family is settled and he has had a great time of it at Celtic. The club has won nine trophies in three years and he has been a big part of that.
"He has come back in even better condition than he was at the end of last season and he has had the bit between the teeth in training."