Lazio clinched a place in the preliminary rounds of the Champions League after finishing third in Serie A last season, but a tough game against Dinamo Bucharest stands in the way of their progression.
And Ledesma's agent has warned the Biancocelesti his client will quit the Stadio Olimpico should Lazio fail to qualify for the competition proper.
"Ledesma will go to Betis if Lazio do not get through the Champions League preliminary round," Vincenzo D'Ippolito said.
Serie A preview
Betis put in a big money bid for the 23-year-old earlier this week, only for Lazio president Claudio Lotito to turn down the offer.
"Betis have offered Claudio Lotito £14m, but they rejected it as they do not want to lose a player that coach Delio Rossi considers to be crucial," D'Ippolito added.
"Cristian has refused offers from other clubs to remain consistent in his choices. Next year, though, we will have to renegotiate his contract with Lazio."
The Argentine moved to the capital in 2006 after having caught the eye in Lecce, where he made nearly 100 appearances over a five-year period. Last season, he netted twice in 33 appearances for the Aquile, becoming a key component of Rossi's side.
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