The 23-year-old has gone from strength to strength since arriving at the club from Vitoria Guimaraes in 2020 and helped Leverkusen qualify for the Champions League last season.
Tapsoba has three goals to boast from 90 games in a Leverkusen shirt and made 19 Bundesliga starts in 2021-22 to help his side to a third-placed finish in the top flight.
Tapsoba's domestic season was disrupted by injury and the Africa Cup of Nations, but he has nevertheless attracted glances from across Europe.
The Burkina Faso international still has four years left to run on his deal with Leverkusen, who are therefore under no pressure to accept a cut-price fee this summer.
According to FootballTransfers, Arsenal have now shown an interest in signing the 6ft 4in defender and are preparing to approach Leverkusen with an official bid.
Arsenal supposedly tried and failed to prise Tapsoba away from Leverkusen in 2021, and the German club could demand as much as €50m (£42.5m) to part ways with the 23-year-old.
The report adds that Arsenal are prioritising a move for another centre-back before the transfer window shuts, in spite of William Saliba's return from his third loan spell away from the club at Marseille.
Les Olympiens were unable to sign Saliba on a permanent deal, and Arsenal are now hoping to tie the 21-year-old down to a new contract, with his existing deal up in the summer of 2024.
Gabriel Magalhaes, Ben White and Rob Holding are also fighting for game time in Mikel Arteta's backline, while Pablo Mari is widely expected to leave.
There was talk of Juventus trying to tempt Gabriel away from North London, and the Old Lady were willing to offer Adrien Rabiot as part of a player-plus-cash deal.
However, Arsenal are not interested in parting ways with the Brazilian, who is also settled in North London after arriving from Lille in 2020.
The Gunners were involved in a two-horse race for Ajax's Lisandro Martinez with Manchester United, but the Red Devils are now confirmed to have won the race for his signature.
As a result, Arteta and Edu have turned their attention to Oleksandr Zinchenko and have supposedly reached a verbal agreement with Manchester City over a £30m deal.
Arsenal will begin their pre-season tour of the USA against Everton in the Charm City Match on Saturday night before meeting Orlando City and Chelsea in the Florida Cup.