While it has been reported in the Midlands that PNE tabled a £400,000 bid this week for the Wales international, that is wide of the mark.
The Lilywhites have had contact with Walsall but only to enquire about the Saddlers’ asking price – believed to be around £750,000.
It is unlikely that North End would go that high for a player who has only 12 months to run on his contract.
Their interest in Bradshaw goes back to the January window.
Walsall were chasing promotion at the time and understandably did not want to let him leave.
With them beaten by Barnsley in the play-off semi-finals, and with time ticking by on his contract, they might be tempted to cash in now.
North End will naturally have other targets as well as Bradshaw, and are spreading the net wide in their search.
Ideally, they would like to sign two strikers to compete with Jermaine Beckford, Joe Garner and Jordan Hugill.
Were they to eventually land Bradshaw, he would have to prove himself in the higher division.
Bradshaw was hoping to be in Wales’ squad for the Euros, having made their 30-man training squad.
But on Wednesday, a calf injury forced him to fly home from the Welsh training camp in the Algarve. Bradshaw has scored 40 goals in his two seasons with Walsall, having joined them from Shrewsbury.
Before that, he played for Aberystwyth in the Welsh League.
Having signed goalkeeper Chris Maxwell soon after the end of the season, North End expect that it will be early next month before they do more business.
The end of May is often a quiet time for transfer dealings, with the play-offs still going on and players being away on holiday.
There are another five weeks of the summer break before PNE report back for pre-season training on June 30.
Preston’s assistant manager Glynn Snodin says they are looking to strengthen several areas of the squad.
Snodin told the Evening Post: “It is important that you get your recruitment right.
“We are looking at a lot of positions.
“If the right player comes along at the right price and fits into what we want to do, we will try and do it.
“Any new player has to be able to fit in to what we do, both on and off the field.
“We have built a special team spirit here and you have to be careful not to upset that.
“When it comes to looking at players, you do your homework on their ability, their mentality and the type of person they are.
“We think we’ve had a great season and now it is about going again for the new one.
“It is not a case of resting on our laurels after what we have done this season.
“We want to improve and push on in what will be a very competitive division.”