As a result of last season's fourth-placed finish in the Premier League, the Magpies have secured a spot in the Champions League group stages.
Eddie Howe has reacted to that achievement by bringing in the eye-catching additions of Tino Livramento, Sandro Tonali and Harvey Barnes.
However, Howe has constantly referred to Newcastle being required to remain on the right side of FFP, something which now requires more work with a further £134m having been spent this summer.
Although Allan Sanit-Maximin has been sold to ease those matters, Howe has recently indicated that he would like to acquire one more player to strengthen his squad later this month.
According to The Telegraph, Howe holds an interest in each of Arsenal's Tierney and Chelsea's Cucurella, both of whom can play at left-back.
Tierney did not feature in the Arsenal squad for their 2-1 victory over Nottingham Forest at the weekend, while Cucurella was a late introduction as a substitute as Chelsea earned a 1-1 draw with Liverpool.
While Tierney has spent the last four years at the Emirates Stadium, it has been suggested that he could be sold having become second choice behind Oleksandr Zinchenko.
Furthermore, Jurrien Timber was preferred in that role when Zinchenko did not start at the weekend, another indication that the Scotland international has dropped down the pecking order.
Meanwhile, Cucurella endured a disappointing first campaign at Stamford Bridge after leaving Brighton & Hove Albion for West London in a deal worth in excess of £60m.
Cucurella appears in line to stay at Chelsea on the basis that Lewis Hall is joining Crystal Palace on a season-long loan deal, with Ian Maatsen the other designated left-sided player in the squad.
Nevertheless, Newcastle are allegedly ready to propose a loan deal with a small fee, as well as an option or obligation to buy at the end of the season.
Much may depend on Chelsea's willingness to entertain a deal when they have to make cutbacks on the basis of shelling out a British-record fee on Moises Caicedo, but Cucurella has also indicated that he is committed to remaining at Chelsea.