The gifted 31-year-old is out of contract at Boca Juniors and has stalled on an expected move to Brazilian side Flamengo because of a raft of interest from South American and European sides.
Renewing with his current side is not out of the question, but Riquelme is also said to have an offer from a second, unnamed English side.
The former Villarreal star almost signed for Everton three years ago, but instead clinched a move from Spain back to his homeland.
Fiery Riquelme missed out on Argentina's World Cup party after a clash with coach Diego Maradona.
Brazilian sides Cruzeiro and Flamengo are also interested, as are Mexico's Atlas, and Buenos Aires side Racing Club de Avellaneda.
Flamengo are believed to have offered him a two-and-a-half year deal worth £45,000 a week.