The 20-year-old midfielder, who spent last season at Scottish League side Clyde, has been featured in three pre-season friendlies for Wrexham since joining on trial.
Manager Brian Little is eager to take a further look at Smith, first team coach Martin Foyle said the Reds are hoping to finalise a deal for the midfielder, who began his career at Port Vale.
"The gaffer is putting something together for Christian. Hopefully he will come in on a short term or non contract basis," said Foyle today. "Christian has played a couple of games and done very well.
"As a left footer he gives us a bit of balance. We want to have a further look at him, he deserves his chance and now it is up to him.
The ball is in his court. Christian has got to fight to get into that group of players, but it is there for him."
Wrexham go into their opening Blue Square Premier match of the season - against Stevenage at The Racecourse on Saturday - on the back of an emphatic 6-0 win at Stafford.
Little gave a hint to what his starting eleven will be for the visit of Stevenage with his team line-up at Stafford, while a further seven players - including trialist Smith - making substitute appearances.
And Foyle was delighted to see players such as out-of-favour Michael Proctor, the injured Neil Taylor and Kyle Critchell, suspended for the opening three matches of the season, present at Marston Road at the weekend.
"The attitude was tremendous of the lads not involved," said Foyle. "They came down to watch and it shows we have got a good team spirit regardless of who is in the side.
"We have to pull together if we are going to do something. From a coach's point of view, the attitude here is spot on.
"We are all raring to go and we will be down to 16 players on Saturday. But there are a lot of games coming up in so we need everybody."
- Wrexham today played a behind closed doors friendly against Hereford which mainly featured players not involved at Stafford.
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