The pair will return to Birmingham on Saturday, just hours before Villa’s Premier League visit of Everton.
Goalkeeper Martinez and record buy Buendia have been training in Croatia following international duty with Argentina to avoid being forced to quarantine in the UK.
Villa did not want them to travel to South America for Argentina’s three World Cup qualifiers but were forced to compromise after the players made it clear they were going.
Smith said: “We are expecting them to join us tomorrow morning and I’ll assess it then and decide if they’ll be involved or not.
“We have got their numbers of what they have been doing each day. That gets sent straight to the performance department and passed onto the coaches. They are in a good place physically which is what we need to know.
“I’ll assess that in the morning and wait until tomorrow.”
Without them, Villa lost 3-0 to Chelsea last weekend with Tyrone Mings at fault for the second goal when Mateo Kovacic pounced on his poor backpass to score.
But Smith defended the England international and insisted he has responded.
He said: “I’ve not had to help him, I thought he dealt with it really well. He owned the mistake and held his hands up to the players and owned it on social media as well. He made a mistake, they happen in football.
“He has probably saved us 20-odd times before he made a mistake. As long as he keeps learning, and from what I have seen in training this week he has, he will keep getting better as a player.”
Everton are unbeaten having won three of their opening four games under Rafael Benitez and Smith knows his side need to overcome the Toffees this season to reach their goals.
“After getting promoted, our remit was to stay up and we have progressed from 17th to 11th,” said Smith, who is without youngsters Jaden Philogene-Bidace and Carney Chukwuemeka.
“The next step is the hardest because you have to try to go past established Premier League teams.
“Some of those teams have been top-four teams in the last decade as well, Arsenal, Tottenham and Everton come into that category.
“West Ham did brilliantly last season and we want to emulate that this season if we can.
“We haven’t made as good a start as we would have liked but it’s important the confidence we built up in the Chelsea game, despite the scoreline, is taken into the home game.”