As the A’s start getting back some of their many injured starters, some of them — particularly the two coming back from Tommy John surgery — might wind up in the bullpen.

Manager Bob Melvin suggested before Sunday’s game that because Jharel Cotton and A.J. Puk will have innings restrictions after elbow ligament replacements, relief pitching might be a good option. Cotton already has thrown two rehab outings and will make another Tuesday with Class A Stockton in which he’ll get up to about 60 pitches.

“There are only going to be X amount of innings after Tommy John and some of those, he’s using up right now,” Melvin said of Cotton. “We’ll see what’s in store for him when he’s able to come back.”

Melvin said he could see Cotton and Puk working out of the bullpen. “The guys who had Tommy John, yeah, there’s some serious thought to that, to be able to use their innings and not lose them very quickly,” he said. “That’s being bantered about, yes.”

Results will matter, of course. Just making it through their 30-day maximum rehab stints won’t guarantee a roster spot, and Cotton and Puk would have to be pitching well to join the A’s in whatever role is deemed best.

“For sure,” Melvin said. “We’re not just going to bring guys here just because they’re healthy. They have to perform. We have to think there’s a role for them.”

Jesús Luzardo, who is coming back from a left shoulder strain, likely would come back as a starter, but the A’s will be very careful with the 21-year-old. He wouldn’t be called up unless entirely ready. Sean Manaea is another story: The left-hander, the A’s ace last season, is being brought back slowly after left shoulder surgery, but there is little doubt he’ll be in the rotation when he comes back, likely in July or August.

Manaea said Sunday that he’s throwing two bullpen sessions this week — he’ll start incorporating his slider for the first time Wednesday — and probably will start start facing hitters the following week.

Starter Marco Estrada, out since mid-April with a lower back strain, said he is hopeful he will be able to start playing catch next week.

Briefly: With Stephen Piscotty still out with the stomach flu, Skye Bolt made his first big-league start, batting eighth and playing right. Bolt walked and scored in the seventh. ... Ramón Laureano extended his hitting streak to nine games.

Susan Slusser is a San Francisco Chronicle staff writer.