Richie Gray is due to join up with the Scotland squad in Japan on Monday and could feature in Saturday's opening Test.
The second row is a late arrival after being released to play in Castres' Top14 play-off defeat to Montpellier.
Gray, 26, is expected to take part in Tuesday's training session before the team is announced on Thursday.
"We will wait to see what mental and physical shape he is in," said assistant coach Matt Taylor.
"He has been very good for us lately, so how he turns up will determine whether he comes in to consideration.
"Today's training is not a full-on session in terms of a lot of the contact, it's more about organisation. We have a hard session on Tuesday, when the bulk of the work will be done, and we hope he [Gray] will be involved in that."
Gray is one of only three specialist locks in Scotland's 27-man squad, along with brother Jonny and Tim Swinson.
|Scotland's tour schedule|
|Sun 12 June:||Arrive in Tokyo|
|Wed 15 June:||Travel to Nagoya|
|Sat 18 June:||1st Test v Japan, Toyota City 1920 KO (1120 BST)|
|Sun 19 June:||Travel to Tokyo|
|Sat 25 June:||2nd Test v Japan, Tokyo 1920 KO (1120 BST)|
|*Both Test matches live on BBC Scotland television & online|
Japan warmed up for the first of two matches against Scotland with a 26-22 win over Canada in Vancouver at the weekend.
Kotaro Matsushima and Takeshi Kizu scored the tries, while Yoshiya Hosoda was sent off early in the second half. Yu Tamura kicked four penalties and both conversions.
"They are quick to contact, they try to play a high-tempo game," said Taylor.
"There are a few similarities to how Japan played in the World Cup in some of their shapes and that they are trying to keep the ball in hand. They are kicking a wee bit more than they have in the past, so whether they keep that up we are not sure.
"Japan is only one ranking place below us, they are a very good side. We want to play well and put a marker down.
"We will be looking to go out there and win the game and put in a performance. I imagine both teams will be better for running together the second time around. We will be looking to play well and win."