The Bundesliga side have a substantial transfer budget after selling Kai Havertz to Chelsea for an initial £62m, which could rise to around £71m with add-ons.
While they will also be looking for a replacement for the goal-scoring midfielder, Leverkusen are keen to add a right-sided defender to their ranks and both Bellerin and Aurier fit the bill.
Both Paris Saint-Germain and Bayern Munich are also interested in Bellerin, with PSG reported to have made a £25m for the Spaniard.
Arsenal are willing to sell the 25-year-old but are looking for closer to £35m for him, which is a fee that could put Leverkusen off, despite their recent windfall.
The clubs might end up meeting in the middle, but with PSG ready to make another move, Leverkusen could face a bidding war with the French club.
The Frenchman has also been heavily linked with AC Milan and could be available for around £17m as he is surplus to requirements under Jose Mourinho.
The Portuguese wants to make more signings before the transfer window closes and is keen to improve his transfer budget by offloading the right-back.
Spurs want to add a back-up striker to their ranks to compete with Harry Kane, while Mourinho also wants a midfielder and a left-back.