Villa have rejected several bids for Watkins from Saudi Pro League side Al Hilal this week, but Emery hinted the England striker would be allowed to leave for the right price.
England defender Ezri Konsa is on the verge of sealing his move to Premier League champions Arsenal, while Argentina goalkeeper Martinez has told Emery he wants to go.
Morgan Rogers, Lucas Digne and Youri Tielemans have already been sold by Villa since the end of last season, joining Chelsea, Paris Saint-Germain and Manchester United respectively.
It is a remarkable dismantling of a team that won Villa's first major trophy for 30 years when they beat Freiburg in the Europa League final in May.
"We have an issue with Watkins, it's clear. He is another player; we have had offers for him," Emery told reporters ahead of Villa's Premier League opener at Brighton on Sunday.
"He is our player; I don't want to sell him. It can change because if it is a good option for him, good option for the club and I can replace him in the squad.
"This is the routine we have, and we did before with the players they are losing. With Ollie, he is here, and he has always been up and down in his performance.
"We will see what happens. If he is leaving, it will be for the best in three ways. One is him, another is the club, and another is the team."
Martinez has been keen on a fresh challenge for the last two years, with Villa signing Japan keeper Zion Suzuki as his replacement.
"He transmitted to us the possibility to have another challenge in his career," Emery said.
"Not now, even last year, he was thinking in case he can have one possibility to change and he didn't do it last year, and he performed fantastic with us.
"This year again, he transmitted to us the possibility to have another challenge, and we decided to sign Suzuki because I think he's a fantastic goalkeeper in case Martinez is leaving."
Despite the astonishing turnover of players at Villa Park, Emery insisted the club, who finished fourth in the Premier League last season, have had a good transfer window.
In addition to Suzuki, they have signed Johan Manzambi, Joao Gomes, Matteo Ruggeri, Alejandro Garnacho and Aaron Wan-Bissaka.
"I'm very excited, I think we have had an intelligent market," he said. "We know where we are and we know what we want to do again for the next year.
"This is the priority and this is the motivation I have."