Dietician and nutritionist. It is safe to eat two or three serves of canned or fresh tuna or salmon a week. While pregnant women are advised to avoid eating a lot of fish that is high in mercury, tuna is generally considered to be low in mercury.f you usually enjoy eating a lot of fish, try to balance out the types of fish you have. Combine fresh tuna, sardines, pilchards and trout, with fish that have lower levels of pollutants, such as haddock, red snapper, ling or flathead. Read our full article on eating fish during pregnancy.