Villa boss Martin O'Neill wants to retain the services of the England midfielder and persuade him to sign a new lucrative long-term contract.
And Barry wants to see what O'Neill's transfer plans are this summer before making any decision on his future.
But Villa director Krulak feels it is only fair to allow Barry to leave if that is his wish after 10 years' service with Villa in which he has clocked up nearly 400 appearances.
Krulak said: "Obviously, we are keen to keep our captain - and we will do all in our power to keep him. But at the same time, he plays a huge part in this equation.
"At the end of the day, he needs to want to stay. The very worst thing we could do would be to try and hold onto a player who wants to leave.
"I hope that we can show him that his future is, in fact, at Aston Villa. We will work hard to do just that."