The Gunners have been in talks with Leicester City over signing Maddison for some time now.
However, it seems the deal will ultimately fail with Football London claiming that progress is hardly being made in the talks.
Arsenal knows Leicester is a tough club to negotiate with and there is a good chance that they will not meet their asking price for his signature.
The Englishman wants to join the Gunners, but he will not cause any trouble to achieve his aim.
As the deal appears tough to pull off, the Metro claims that Arsenal has an eye on a move for Lingard.
The Manchester United midfielder spent the second half of last season on loan at West Ham and he was one of the finest players in the Premier League.
However, he would face more competition for a place at Old Trafford following the arrival of Jadon Sancho and he could leave.
The report says United values him at £25m, significantly less than what Arsenal will pay if they want to sign Maddison for Leicester.
However, it remains to be seen if the Red Devils will sell to a direct rival like the Gunners.