The U.S. international looks set to leave Puebla with the Liga MX club placing him on the transfer list.
The 31-year-old is currently with the United States in Kingston ahead of a World Cup qualifier against Jamaica. The winger earned his 100th cap in a friendly against Belgium last week.
But as Beasley works his way back onto the national team, he could be headed out of his current club.
The domestic transfer window in Mexico closes on Wednesday.
Since joining Puebla from Hannover 96 in 2011, Beasley has scored 11 goals in 64 league appearances.