The Vincent and Grenadines international is on trial with the League Two side after being released by Oldham Athletic and score their third goal in the 3-4 defeat against Liverpool at the Racecourse on Saturday.
The 32-year old has said he is enjoying himself at Wrexham.
"I am trying to work on my fitness and if all goes well I could be getting a contract," said Jack
"It was frustrating for me at Oldham Athletic. I did my medial ligaments and was out for nine months. It is very difficult trying to come back and start from scratch but that's what pre-season is all about.
"Hopefully I can work my way back into it, obtain a contract and start playing regularly again.
"Denis Smith is an honest manager and he has told me the situation about where I stand.
"He has told me to work on my fitness, given me the opportunity to train with the team. They are a good bunch of lads, I know some of the players anyway, and if you can fit in it is a great bonus.
"It is always a bonus as a striker to get a goal because you build momentum and confidence. I love scoring goals and hopefully I can do the same for Wrexham."
Wrexham boss Smith has also not ruled out a possible contract for Jack saying: "He wouldn't be here if he wasn't in with a chance of a deal. His fitness levels are poor, he has got to get that better, and if he does we'll see what he can do. We'll wait and see."