When asked Tuesday if he had a few favorites in the 49ers’ 10-man draft class, vice president of player personnel Adam Peters ticked off several players.

Then, he threw out a surprise.

“I do like Hikutini,” Peters said, “even though we didn’t draft him.”

That would be Louisville tight end Cole Hikutini, who was bypassed in the 253-man draft after he posted a plodding time in the 40-yard dash and had just one season with more than 19 catches at the Division I level.

So why is Peters so enthused? The 49ers think Hikutini, who grew up in Sacramento and spent one season at City College of San Francisco, slipped through the cracks of a deep tight end class and is a potentially ideal fit as a pass-catcher in head coach Kyle Shanahan’s system.

“I really liked him just for our offense,” Peters said. “Maybe not everybody’s, but I think as far as what Kyle is looking for in a tight end: A guy who’s a separator that can get open underneath. I saw something in him that, for a guy down the line (in the draft), I thought he had something special. A guy that was better than maybe his numbers suggested.”

The 49ers selected Iowa’s George Kittle, one of the draft’s best blocking tight ends, in the fifth round. And after the draft, they began their aggressive recruitment of Hikutini, whose so-so blocking ability was another reason he wasn’t selected.

According to a post-draft story by MMQB.com, Peters, Shanahan, tight ends coach Jon Embree and general manager John Lynch combined to make at least eight phone calls to Hikutini, who was also speaking with the Patriots, Saints and Lions. Peters focused on Hikutini’s agent, and the 49ers finally landed the top rookie free agent on their list with a $10,000 signing bonus and $100,000 guaranteed.

Hikutini noted the 49ers actually began barraging him in the latter stages of the draft.

“They were contacting me,” he said, “just making sure I stayed near my phone.”

Hikutini took a meandering path to the NFL. After playing just one season of football at Pleasant Grove High, he spent two seasons, including a redshirt year, at Sacramento State. He then spent 2014 at CCSF before landing at Louisville, where he had 19 catches for 348 yards in his first season.

Last year, he grabbed the attention of NFL scouts (50 catches, 668 yards, eight TDs), but suffered a knee injury in a bowl-game loss to LSU that prevented him from running at the combine. He ran a 4.85-second 40-yard dash at Louisville’s pro day and said he still wasn’t healthy.

“I’ve run faster 40s than that, but I wanted to go out and compete,” Hikutini said. “I wanted to show them that my knee was getting better. I think I came out a little sooner than I should have, but I showed them that I can compete.”

In Santa Clara, Hikutini will attempt to fill the pass-catching role the previous regime had envisioned for tight end Vance McDonald, a 2013 second-round pick with 64 career catches. Despite his undrafted status, Hikutini will have the chance to unseat McDonald, who Shanahan and Lynch acknowledged was the subject of trade talks during the draft.

Still, Hikutini has to prove he should have been drafted. Not surprisingly, Peters thinks he’ll do just that

“There are so many tight ends in this draft that guys get kind of pushed down,” Peters said. “And through the process, if they don’t test well, they kind of get pushed down even more. Hopefully, it all works out. I think he’s got a chance to be pretty good.”

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch