Thordarson has signed Patrick Ada and Mat Mitchel-King this summer
Crewe could field as many as five trialists for their friendly against Wigan on Thursday, according to Alex manager Gudjon Thordarson.
Nathan Koo-Boothe and Floribert N'Galula have been training with the players at their Carden Park base.
Thordarson told BBC Radio Stoke: "Two are already with us, and two or three more could be here by the Wigan game.
"I'm trying to bring in a player from abroad as well. Hopefully we'll begin to see a few signings taking place."
Thordarson added: "I'll have a look at them in the few sessions that they are with us. That's important to me, not just to see what they are like as players, but also what their characters are like."
Crewe have only added two players - Histon duo Patrick Ada and Mat Mitchel-King - in the close season, whilst releasing 11 of their squad from last season, and selling Tom Pope and Michael O'Connor to Rotherham and Scunthorpe respectively.
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