Ludlow forward Hodge did his chances of earning a deal no harm at all with a solid display at the Prostar Stadium.
Manager Paul Simpson told the club's official website: "We spoke to Ludlow to see if it was okay for him to come down and have a run-out so we could take a look and they were happy with that.
"He impressed with his performance and I've spoken to Ludlow to see if they are happy for Nathan to come in and train with us for a couple of days and play in another reserve game, and they are okay with that. We will now need to speak to Nathan and see if he would be up for that and how it fits into his work.
"He's an 18-year-old and it's a little concern that he lives in Craven Arms and hasn't been spotted by the club until now."
Shrews also used the Walsall game to have a look at fellow trialist Grant Kerr but Simpson has opted not to take his interest in the midfielder any further.