Velez, the star of one woman show They Call Me La Lupe, will end her limited run in the Off-Broadway production on 23 January (11), after less than three weeks in the role.
The stage show, written by Emmy winner James Manos, Jr. and Luis Caballero and directed by Veronica Caicedo, tells the rags to riches life story of the Latin singer, who became the lead vocalist in Tito Puente's band.
But Velez won't be waving goodbye to the singer just yet - Manos, Jr. and Caballero are in talks with the Puerto Rican Film Commission to shoot a planned movie version with the actress, according to Variety.
Manos says, "I co-wrote this show as a way to jumpstart the process. I felt the play would help revive interest in La Lupe.
"It's scary how Lauren has inhabited her being. Not only does she look like La Lupe but she has captured La Lupe's distinct voice as well."
The star joined the hit TV show in 2005 as Lieutenant Maria LaGuerta, and discovered romance while learning her lines.
She says, "I am in love... Once I got cast, James called me and said, 'Congratulations, I'm really happy you got the part... I'd love to take you out for dinner to discuss the character.'"