Evra's future at Old Trafford has been called into question ever since Sir Alex Ferguson acquired Alexander Buttner, who plays in the same position as the French international.
However, Albiston, who spent 14 years with United, has tipped Evra to "bounce back" from his recent problems both on and off the field.
"Patrice has had a lot to deal with over the last couple of years and I think that has had an effect on his form, but he has the experience to handle the criticism and bounce back," Albinson told the Manchester Evening News.
"He was at the centre of the problems in the France camp at the World Cup in 2010 when he was captain of his country. There was a mutiny and a big backlash in the country when they came home under a cloud.
"It wasn't a healthy situation and Patrice was a big part of that. It can't help.
"Last season there was the unfortunate Luis Suarez affair. Evra was impeccable with the way he dealt with that. Then, just when you thought it was over and done with, there was the non-handshake at Old Trafford from the Liverpool striker.
"The whole episode had dragged on and I think no matter how much you try to shut it out on the pitch, I think it does have an impact."
Evra wears the number three shirt that was worn by Albiston during his spell with the Red Devils.