The attacking midfielder brings a wealth of experience having represented Warrington Town, Marine, Burscough and Witton Albion amongst others.
The former Prescot Cables star joined Linnets in the summer and has also previously represented National League side Telford United.
Monaghan also had a spell playing in Australia for Corio Soccer Club before returning to the UK, he then signed for Witton in 2019.
On his latest signing, manager Michael Ellison said: “We tried to get MJ in the summer but couldn’t manage to get him in, so when the opportunity came to get him in we jumped at it.
“He’s got a wealth of experience at this level, he will be a great addition to the squad and certainly give us more options at the top end of the pitch.
“I’m looking forward to working with him."
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