It is understood that the 33-year-old began training with the Welsh club this week and is set to spend the coming days with the National League side.
The club, that currently sits 7th in the National League, are bankrolled by Hollywood stars Ryan Reynolds and Rob McElhenney, so could well be in a position to offer Tomlin a permanent deal.
It would be a sensational coup for Wrexham as they look to get back into the EFL for the first time since relegation in 2008.
Tomlin has been without a club since leaving Cardiff by mutual consent in October.
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He appeared 177 times for Posh, across two spells, scoring 45 goals and helped the club achieve promotion to the Championship via the play-offs in 2011.