Valencia defender Alba spent time at the Catalan side as a youth player, but left in 2005 and has since developed into an accomplished left-back at both club and international level.
Meanwhile, Martinez played a key role in 2011-12 for Athletic Bilbao, which saw the Basques reach the finals of both the Europa League and the Copa del Rey, only to lose to Atletico Madrid and Barcelona in each.
"Let's hope [Barca] sign [Alba]," he told Mundo Deportivo. "He's a magnificent player with great projection.
"He is complete, can play as either a winger of a full-back, is quick, has a great left foot, gets to the byline and crosses well.
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"He would adapt very quickly at Barca, so let's hope he can come in. He would be a great signing."
On Martinez, he added: "Even though he is young, he has a lot of experience. He is agile and a very good player. He would also be a very good signing."
Barcelona finished second in La Liga last season, nine points behind arch-rivals Real Madrid, and their disappointing season has prompted talk of reinforcements arriving at Camp Nou this summer.