Police are investigating how Laura Plummer, the British woman who was convicted of drug smuggling in Egypt, obtained nearly 300 Tramadol tablets.
Humberside Police announced it was "looking into the circumstances of how the prescription drugs came to be in her possession".
Plummer, 33, was sentenced to three years after being caught with the painkillers at Hurghada International Airport while visiting her partner.
The Hull shop employee told Egyptian authorities that she obtained the tablets from a colleague and that they were meant for her partner Omar Caboo to treat his back pain.
"Following the arrest and subsequent conviction of Laura Plummer, we are looking into the circumstances of how the prescription drugs came to be in her possession and if any further individual has committed any offences," Det Insp Jon Cross said.
"This investigation is still ongoing. If you have information you believe could assist us in this inquiry, please call 101."
Tramadol, a strong painkiller, is available on prescription in the UK but is banned in Egypt. She claimed to Egyptian authorities that she had "no idea" the tablets were illegal.
Det Ch Sup Judi Heaton said that passing on the drug "is not necessarily a criminal act but it is a civil offence under the Medicines Act".
The Foreign Office said it was hoping to arrange a prison transfer for Plummer. She was being held in a notorious prison in Qena, prompting her family to raise their concerns about her safety.
Plummer's sister Rachel commented on her prison transfer, saying: "No prisons are nice but I think Qena's the bad one."
It is believed that Plummer will appeal her three-year sentence.