Paqueta was a standout performer in Les Gones' underwhelming 2021-22 season with 11 goals and seven assists in 44 matches across Ligue 1 and the Europa League.
The former AC Milan starlet found the back of the net nine times in 35 Ligue 1 appearances, but Peter Bosz's side could only muster an eighth-placed finish in the division.
Paqueta has unsurprisingly been linked with an exit from Lyon following their failure to qualify for Europe, and a move to Newcastle United has been strongly mooted.
The Magpies would not be able to offer the Brazil international the chance to play on the continent either, which could work in Arsenal's favour in negotiations.
According to Goal, Arsenal technical director Edu has touched base with Paqueta's representatives to formally register the Gunners' interest in signing the playmaker this summer.
However, Paqueta - who has been utilised in a variety of positions in the final third during his time at Lyon - still has another three years left to run on his contract at the Groupama Stadium.
As a result, Lyon are prepared to demand as much as €80m (£67.8m) to part ways with Paqueta, and Arsenal are yet to approach Les Gones with an official bid.
The French club have reportedly accepted that it will be difficult to find a club willing to fork out the entirety of their asking price, but Arsenal's first offer is likely to be rejected either way.
Tottenham Hotspur were previously linked with a swoop for Paqueta but are not expected to reignite their interest after spending £60m to sign Richarlison from Everton.
Paqueta's compatriot Bruno Guimaraes left Lyon to head for St James' Park in January, and the former has been pictured alongside the midfielder in Newcastle, fuelling speculation over a summer move.
Lyon president Jean-Michel Aulas has confirmed that his side have received offers for Paqueta, telling reporters: "There are offers for him. There are some players who can feel fully fulfilled in the project, and others who are not.
"Economically, we have the means to pursue our ideas and our objectives. The coach gave us his opinion and there is also what the players want to do."
Manager Bosz has also admitted that Paqueta is not guaranteed to remain at the club for the 2022-23 season, adding: "Lucas is a very important player, but it depends on what the player wants. I've already had a conversation with him, but that will remain between us."
The former Flamengo youngster arrived at Lyon for an £18m fee in the summer of 2020 and has registered 21 goals and 13 assists in 77 appearances for the French giants over the past two seasons.