Posh owner Darragh MacAnthony revealed on Twitter on Tuesday evening that PNE had made three bids for 26-year-old Hughes, all of which had been turned down.
Replying to a question from a Peterborough supporter about whether North End were interested, MacAnthony tweeted: "Just had confirmation, we have had 3 bids from them today for him from Preston. All turned down. Cheers."
North End are in the market for a left-back having sold Greg Cunningham to Cardiff City last week for a fee in the region of £4m.
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Cardiff-born Hughes started his career with Newport County before joining Peterborough in June 2016.
Last season he made 56 appearances for Posh in all competitions.
The 6ft 2in defender can also play in the centre of defence.