Rovie

You may be looking for the enhanced Rovie that plagued the Fifth Doctor.

A rovie was a type of Gallifreyan mouse. Ordinarily, they possessed no more abilities than their Terran counterparts, though they were longer-lived. They had fairly limited intelligence and a fifteen second memory. They could be domesticated and in early Gallifreyan history they were used in experiments. Some Time Lords kept them as pets.

The Fifth Doctor, Erimem, and Shayde once encountered a rovie that had become lost in the Doctor's TARDIS and subjected to the raw power of the Time Vortex. Though such exposure should have killed it, it made it evolve rapidly. It developed sentience, the ability to speak and a massive intelligence. It tried to take over the TARDIS and with it the universe. With Shayde's assistance, the Doctor managed to disrupt the rovie's control of the TARDIS. Shayde then took it back to Gallifrey for further study. (AUDIO: No Place Like Home)