Dubbed by some the Colombian Cristiano Ronaldo, Muriel is currently on loan at Lecce from his parent club Udinese.
The 20-year-old is rated at £8 million ($12.7m) and has also attracted interest from Barcelona, Milan, Juventus, Napoli and Roma, according to the Mail;'s report.
Earlier in the month Muriel spoke of his interest in a possible move to the current Serie A leaders.
I really like Milan. However, I am focusing on Lecce for now, he told Tuttosport, according to Goal.com.
Muriel enjoyed a meteoric rise after just a handful of first-team appearances in his native Colombia with Deportivo Cali. Following a hat-trick in only his third game, European clubs came calling, with Udinese snapping him up for €1.5million ($2m) in the summer of 2010, according to imscouting.com.
After spending last season on-loan in the Spanish second-tier with Granada, Muriel has impressed with five goals in 18 starts for Lecce this campaign. He also scored four goals in five appearances during the Fifa U-20 World Cup in his home nation last summer.
Udinese have an incredible track record of plucking young players from South America and turning them into future superstars. One of those, Alexis Sanchez, is now starring at Barcelona, after a €43 million ($57m) transfer from Udinese last summer.
Arsenal are known to be looking to bolster their squad, particularly up front where there is too much reliance on Robin van Persie.
German forward Lukas Podolski has reportedly already agreed to join the club in the summer, although with the current-Koln star also able to play wide on the left, Wenger is likely to want another striker to add depth.
If Arsenal are to face competition from the likes of Barcelona and Milan for Muriel's signature then it will be hard for the Gunners to complete a deal. If given the chance, though, Wenger will likely emphasize the club's excellent record of developing young players and giving them a chance in the first-team.