The 20-year-old opted not to renew his contract with Paris Saint-Germain last year and headed back to his homeland, joining Ruud van Nistelrooy's side on a free transfer.
Simons has made a name for himself in the Netherlands over the past year, scoring 19 goals and setting up 12 more in 46 appearances across all competitions during a stellar campaign.
The former Barcelona starlet has 16 goals to show from 32 Eredivisie matches in the current campaign, the joint second-most in the division and only behind Anastasios Douvikas's 17.
Simons also contributed one goal and two assists to PSV's KNVB Beker triumph, setting up Thorgan Hazard's equaliser in the final against Ajax as Van Nistelrooy's men prevailed on penalties.
PSV are under little pressure to sell Simons for a cut-price fee this summer, as his contract runs for another four years, but clubs across Europe are supposedly queuing up to present their offers.
According to The Mirror, Arsenal will be presented with the chance to bring the midfielder to the Premier League this summer, and he is already pondering a move away from the Eredivisie on the back of his breakthrough campaign.
Simons recently switched agents and is now represented by Doubled, whose owner Darren Dein is the son of former Arsenal vice-chairman David Dein, and the Gunners could therefore emerge as the front-runners to sign the starlet this summer.
PSG are understood to have inserted a buyback clause into Simons's deal when he made the move to PSV, and the French champions would supposedly need to pay just £10m to bring him back to the Parc des Princes.
However, the report adds that PSG have not shown any intention of triggering the option, and Simons himself may not even be keen on a move back to the French capital given his lack of previous opportunities there.
The Netherlands international made just 11 senior appearances at PSG between 2019 and 2022, but he has since earned plaudits for his performances in a variety of roles under Van Nistelrooy.
Simons has operated as a number 10, centre-forward and winger for PSV, who claimed a 2-0 win over Arsenal in the group stage of the Europa League in October, where the 20-year-old completed the full 90 minutes.
The 2003-born youngster's exploits in the Eredivisie have also caught the eye of the national team, and he has now earned three senior caps for the Netherlands, making his debut at the 2022 World Cup.
Arsenal will prioritise midfield signings this summer and could soon wave goodbye to Granit Xhaka, who is believed to be close to a £13m switch to Bayer Leverkusen.
Simons's versatility would also come in handy amid speculation over the futures of Reiss Nelson and Folarin Balogun, while Nicolas Pepe does not have a long-term future at Arsenal either.