The former Athletico Bilbao player, who has been in tremendous form since joining the Somerset outfit during the summer, was invited to Aldershot for a two-day trial this week, the website revealed.
"When you're doing well you expect other clubs to come after your players," said Bridgwater manager Craig Laird. "It's part of the game.
"Olondo would obviously like to get back to playing on a full-time basis. It's no a problem for us because when a player leaves it opens the door for another.
"You cannot blame players who want to play at a higher level.
"He's already shown his class since joining us."
Olondo goes to the University of West of England and was brought to the club by assistant-manager Danny Phillips, who runs the university's football side.
The player, who scored twice at the weekend against Burnham, has also spent some time on trial at Bristol Rovers.