The 28-year-old singer visited Afghanistan recently as part of a morale-boosting trip for The Pride of Britain Awards - and after her visit Cheryl revealed that she had returned with a phone number from one of the soldiers.
She said: 'I think I am going to call him this week and we'll see what happens.
'I'm sure he's not expecting me to ring but that's why it'll be funny - and that's why I'm going to do it.'
According to British newspaper the Daily Mirror, the Girls Aloud star was introduced to Andy at an awards presentation, and again at an informal dinner.
Baker's brother-in-law Graham Peck said that Andy, 25, had been 'raving about Cheryl', and made one of his pictures with her his Facebook profile picture.
Graham said: 'Andy would love to take Cheryl out for dinner when he's back in the UK. He thought she was absolutely lovely, and really gorgeous - I think all the guys did.
'They met up a couple of times during her trip and hit it off.'
But Andy, who has been in the Marines for four years, is worried that he will miss the Promise This singer's phone call because he has no phone service until October 1.
Peck added: 'When Bagsy read that Cheryl was planning on ringing her mystery soldier, he panicked because he's not allowed to have his phone on for another nine days - it's military rules.
'He wants her to know that he'll be in touch the moment he lands, and wants her to wait for him. Andy's a great guy and keeps himself fit in the gym.'