Heckingbottom has made a new central defender his priority in the January transfer window but has already missed out on several targets, including James Hill and John Souttar, who joined AFC Bournemouth and Rangers respectively.
And with just five days left before the window shuts, there are no new developments.
"We are no closer,” said Heckingbottom.
"It’s frustrating, obviously, but we’re no closer.
"There’s been lots of different reasons why we’ve not got one over the line, whether that’s players changing their minds or competition from other clubs, money, us being a little bit slow and letting someone else nip in.
"There’s been a combination of a lot of things.”
Heckingbottom confirmed Liverpool defender Rhys Williams is ‘one of many’ targets – but the 20-year-old is not currently available.
"As far as we know he’s not available as it stands,” Heckingbottom said.
"He’s Liverpool’s player and we just have to keep monitoring lots of players who we think could come in and do a good job for us.
"There are a lot of players out there but we have to be clear of the role we want them to perform.”
Any move for a defender in this window is likely to be a loan, Heckingbotton confirmed, with no budget to bring in a player permanently ‘as it stands’.
He added: "Ideally – and I’ve said it all along – we want players to be our players. We want to be buying our own players and not plugging the gaps with loans.
"But that may become a necessity.
"The priority was – and is – to work with our own players and develop our own.”
United are concentrating their efforts solely on a defender before Monday’s 11pm deadline.
"We are an injury or illness away from potentially being in trouble,” said Heckingbottom, who also spoke of his reservations about entering into loan agreements which specify that temporary recruits must play.
"We might get ourselves in a really good position this season and it’d be a crying shame if then we couldn’t capitalise on it because we get an injury or illness at the wrong time to one or two key people.”