La Razon says Arsenal will soon be stepping up their efforts to secure the services of Rodriguez.
The Gunners are believed to be planning to begin negotiations with Betis over a move this summer in the coming days.
Rodriguez has a release clause included in his contract for £69million - which could prove a problem for Mikel Arteta's side.
However, the Premier League club are due to start their bidding at around £25.7m and hope to entice Betis into business.
Arsenal are looking to recruit at least one new midfielder over the summer as Arteta plots his rebuild.