The Brazilian defender feels the Bluagrana would be wrong to allow the two attackers to depart this summer, while he remained coy on the future of Neymar
Villa, 31, has been linked with a move to Premier League giants Arsenal, while the 24-year-old Alexis has caught the attention of Juventus and Inter.
However, Alves believes Barca should do their utmost to hold on to the duo as he feels they still have an important role to play at Camp Nou.
"If it was down to me I would strengthen rather than sell what we have because we're very happy with them [Villa and Sanchez]," the Brazilian told DPA.
"Both are great professionals and that's what counts."
Alves was also questioned about Neymar's future, but decided to keep his thoughts to himself in order to avoid any controversy.
"That's something I've put on hold. I don't want to talk about it because I cause a stir every time I speak."
Neymar will travel to Barcelona in July to discuss a potential transfer, as exclusively revealed by Goal.com earlier this week.