Lately, every step along the rehab program trail has left a smile on Luis Severino’s face, and Thursday wasn’t different.

“Today went well, hopefully Sunday goes well,’’ Severino said following a 30-pitch afternoon bullpen session ahead of the Yankees and Indians opening a four-game series in The Bronx.

Severino showed increased intensity with his pitches and said he threw all his pitches. With Aaron Boone watching, the former staff ace was pleased.

“I am glad and happy the velocity is there,’’ said Severino, who hasn’t pitched in a game at any level this season with an inflamed right rotator cuff that developed in spring training and a right lat problem that surfaced later.

The next step for Severino is facing hitters in a simulated-game setting Sunday at the Stadium before the Yankees travel to Oakland for a three-game series against the A’s.

“After that head to Tampa,’’ said Severino, who wants to build up to 60-75 pitches to be ready for big-league work. “Right now I feel better than spring training. I let go of a couple to see how my arm feels.’’

GM Brian Cashman agrees with Severino that at some point he will be an active major league pitcher, but as usual in a situation like Severino is in, there is always a pause.

“What jives is at some point a major leaguer, yes,’’ Cashman said. “I am not going to echo his commentary, but I do know that he is progressing and we are certainly hopeful. We like to get him along with a lot of other high-end players back to join the party. Get as close to full throttle as we can. But [Severino] slowly but surely we will able to deploy him at some point.’’

First, Severino’s health will dictate when or if he gets back. Then there is the landscape of the staff to consider. Will he be built up to start or be used out of the pen?

“Like everything else, it will depend on where we are at and what our needs are. Can we buy more time or not as we navigate what is our best interest in the present and the future. We will be in a better position to collaborate with him what our roster is and how close he is,’’ Cashman said.

Since Severino is 41-25 with a 3.51 ERA in 96 games (85 starts) since 2015 and 33-14 in 2017-18 with a 3.18 ERA while logging 384 ²/₃ innings, the Yankees would certainly look forward to adding him to the mix as they head into October as likely AL East champions. And they would take their chances in the postseason despite Severino’s spotty October ledger. In six postseason games, Severino is 1-2 with a 6.26 ERA and has allowed 36 base runners (14 walks; 22 hits) in 23 innings and has worked past 4 ²/₃ innings once. He registered one out against the Twins in the 2017 AL wild-card game and gave up three runs. His last October appearance was against the Red Sox in the 2018 ALDS when he got pummeled for six runs and seven hits in three innings of Game 3, which the Yankees dropped 16-1.

“He has been one of the better starters in the game, so to get our hands on that type of ability is something we are currently dreaming on,’’ Cashman said. “At the same time, I don’t want to put the cart ahead of the horse by asking too much from someone who hasn’t played for us yet. He is healthy now and he has to get built up. The potential of him reaching his ceiling would be very exciting for us. When he is right and when he is on, we know what he is capable of. It’s pretty special.’’