The 24-year-old England international has been restricted largely to substitute appearances in the Premier League this season, with his only starts coming in the Community Shield and Carabao Cup.
His lack of regular football has prompted clubs to monitor his situation ahead of the January transfer window, with a loan move potentially under consideration.
Atletico Madrid and Juventus are among the clubs understood to have admired Madueke for some time, although other sides could enter the race if his position at Arsenal remains unchanged, says the Telegraph.
Madueke was part of England's World Cup squad during the summer and started the quarter-final against Norway, but his reduced role at Arsenal has since contributed to him missing the latest Nations League squad.
Thomas Tuchel's England staff regard Madueke as one of the country's best one-on-one forwards, but competition for places has made regular football difficult to secure at club level.
Mikel Arteta has a number of attacking options available to him, while the arrival of Christos Tzolis has added further competition. Max Dowman has also emerged as another option capable of pushing for senior opportunities.
Madueke joined Arsenal from Chelsea in a £48.5 million deal last summer after spending 18 months at Stamford Bridge. He had previously broken into senior football with PSV Eindhoven.
The winger made 16 Premier League starts last season, although a knee injury kept him out for around two months and restricted his overall involvement.
Arsenal are not believed to be actively looking to sell Madueke, but a temporary move could give the England international the regular football he needs if his situation does not improve.
A January loan would also allow Arsenal to retain control of a player who still has significant value and could return to compete for a starting place after gaining more experience elsewhere.
For Madueke, the next few months will therefore be important as he attempts to force his way back into Arteta's plans before the January window opens.