Moyes is in Seattle with his squad preparing for Sunday's prestige friendly against Argentinian giants River Plate which will be played in Edmonton, Canada.
But the lack of numbers in his squad is clearly worrying Moyes, who has major injury problems still to be resolved over Mikel Arteta, Ayegbeni Yakubu, Phil Jagielka and Victor Anichebe, none of whom will be fit to start the season.
Lawrie, 18, already capped at senior level by Northern Ireland, does not fall into the category of first-team squad potential yet.
He will be assessed over the next few days with a possible decision on a transfer not likely until next week.
Lawrie was involved in 26 games for Vale last season, the vast majority as a substitute, and is rated one of the best youth products at the Potteries club for many years.
He made his international debut last month as a substitute against Italy, and Vale chairman Bill Bratt said: "Everton asked if they can have James for a week to see whether they would be interested. We cannot stand in his way and we wouldn't want to.
"Every young footballer wants to play in as high a level as possible, so he goes with our blessing and, hopefully, the lad will make it.
"He has come through the ranks here and done his best for Vale, but he has to look to his career. We have to understand that."
Lawrie could be one for the future, but Moyes has more pressing problems while still insisting he has no intention of selling Joleon Lescott to Manchester City.
"We have got a decent team but we have a concern as we have only got two fit senior centre-backs at the club just now," Moyes said.
"That means I am going to have to add a central defender. It is a priority and we do not have cover at left-back either.
"Joleon could cover for Leighton Baines but we just do not have the options to do that at the minute. There is a shortage there (at full-back) as well.
"And we do not have Mikel Arteta fit, nor do we have Yakubu, Jagielka or Anichebe fit so our numbers are dramatically down, it is something we need to address."
Moyes failed in his attempts to sign England Under-21 full-back Kyle Naughton this week, losing out to Tottenham.
However, he does not think he will struggle to attract players to Goodison Park.
"I am pretty sure that players will be keen to come here. They will see a club that has improved and will go on improving," Moyes added.
"You only have to look at the squad we have got to see that the players have made progress, they are a hard-working group and hugely determined.
"The market is quiet at the minute and only Manchester City seem to be buying big but I think that others will start buying before too long.
"We know that we have got to add players. Yes, I would have liked them in before now, but I will definitely be adding to the squad as soon as the right one becomes available."
Moyes has no injuries among the travelling squad, and Tim Howard, Joseph Yobo, Jack Rodwell and Steven Pienaar are likely to be given their first action of pre-season against River Plate.