Martin is one of three uncapped players in the 26-man squad for tonight's game at Craven Cottage in London and the English-born 25-year-old, who is eligible through his Scottish father, is likely to feature after scoring 25 times for Derby this season.
But after losing to Queens Park Rangers in the play-off final on Saturday, Derby called their players in to attend a civic reception on Monday, which delayed Martin's arrival with the Scotland squad. That meant he missed two of Strachan's training sessions and worked with his new team-mates for the first time yesterday. That lack of familiarity seems likely to persuade the manager to leave Martin out at kick-off.
"The English play-off final can be either the best or worst game in the world," said Strachan. "Unfortunately for the Derby lads [Martin, Craig Bryson and Craig Forsyth are all in the Scotland squad] it was the worst. But I've said to them that a lot of teams who fall at that hurdle go on to do well the following season.
"I had been keen to get Chris Martin in on the Monday, to do the two sessions and have a good look at him. But we have only seen one session with him; albeit it was terrific. I had hoped to see how he did alongside the likes of Shaun Maloney and Scott Brown over a couple of sessions. But Derby wanted to keep the players back, for whatever reason. So that has altered my thinking on it a wee bit. The stuff he showed this morning was first class, but I don't know if it is long enough. With Craig [Bryson] it's a question of fitting him into a system. He has a certain system he likes to play. But we have good players who are not getting into the team because they don't fit into our system at the moment. It would be great to be able to use them."
Scotland's final match of the 2013-14 season will be a stiff test - Nigeria are about to compete at their fifth consecutive World Cup. Strachan has been keen to ensure the players' tempo is maintained.
Having worked so hard to create a sense of momentum around the national team, reflected by the current five-game unbeaten run, there is no desire to see it tossed away cheaply. There was a double session on Monday and Strachan had planned the same yesterday but changed his mind because the training pitch had been affected by heavy rainfall.
"With the intensity of the work they produced in the morning, added to the surface water at the training pitch, we decided enough was enough," he said. "We will now do more than we normally do in the morning session before the game. There are a couple of things I need to look at before I meet the boys again.
"There is absolutely no end-of-season feel to it. It is actually more a beginning-of-the-season standard they have brought to training. That has been helped by the ones who have not been here before, like Peter Pawlett and Mark Reynolds, along with Craig Forsyth and Chris Martin who joined us this morning for the first time. The ones who have been in the squad for a while also want to impress the new guys, so there has been an intensity.
"I don't think we would have got that if we'd gone to South America for a couple of games, which was another option. Nigeria are physically strong. I would imagine everybody wants to be in that starting line-up ahead of the World Cup."
Nigeria manager Stephen Keshi will cut his provisional World Cup squad by seven players after the Scotland game. "We are not going to Brazil just to make up the numbers as we know that the World Cup is a serious business," he said. "We would not let the country down, never.
"We are delighted to be playing the Scottish team in London as part of our pre-World Cup preparations. We know it will be a real test in front of a passionate crowd. We hope that many London-based Nigerians will come out en masse to give the Eagles a rousing send-off ahead of Brazil."
Scotland (possible) Marshall, Hutton, Greer, Hanley, Robertson; Bannan, Brown, Morrison, Anya; Naismith, Maloney