Stephen Vogt is so multitalented, he can even make a plug for his All-Star worthiness by channeling Chris Farley’s Matt Foley, motivational speaker.

Vogt, the A’s catcher and team leader, appeared on the MLB Network’s “Intentional Talk” last week and again showed off his gift for mimicry, this time unleashing Farley’s “van down by the river” character from “Saturday Night Live.” At the behest of hosts Chris Rose and Kevin Millar, who had loved Vogt’s NBA ref routine last year, Vogt wound up in the strange situation of talking himself up — as someone else.

“It’s hard to talk about yourself, I don’t like doing it,” Vogt said with a chuckle two days later. “But the All-Star Game would be cool, obviously. I’m not going to say it wouldn’t mean anything to me, it would be a huge honor, given where I was a year ago, two years ago.”

Where was Vogt a year or two ago? Not on anyone’s All-Star radar, that’s for certain. He wasn’t on the A’s Opening Night roster last season. The year before, he was traded from the Rays to A’s but spent most of the season at Triple-A Sacramento.

Twice, Vogt’s wife, Alyssa, talked him out of hanging it up.

“I’ve literally had the phone in my hand to call teams and ask about positions in player development and she’s said, ‘Give it another year,’” said Vogt, who is second behind Kansas City’s Salvador Perez in American League All-Star balloting released Monday.

The A’s have had plenty of unusual success stories in recent years — Brandon Moss, Josh Donaldson, Sean Doolittle — but out of nowhere, Vogt is the A’s best player and a potential All-Star at 30. That seldom happens.

“Boy, it’s all coming together at one time for him,” A’s manager Bob Melvin said. “You look at the numbers across the board for him and especially as a catcher, he’s probably as productive as anyone in the game right now.”

Vogt is in the top 10 in the league in several offensive categories — and entering Monday he was tied for second in RBIs, with 38, and was second in OPS, with a 1.022 mark.

“There are only a handful of guys in the game who can catch as well as Vogter does and hit as well as he does — they’re hard to come by,” A’s reliever Dan Otero said. “He’s one of the best players in the league right now, hell, yeah he is — and as a catcher.”

Vogt appears to be a classic late bloomer, but he always hit in the minor leagues. He just didn’t have an everyday position in Tampa Bay’s organization, where more highly rated catching prospects got most of the innings. He wound up playing as much or more at first base and in the outfield, which is why he is so versatile now.

The key for Vogt, just as it was for Moss, Donaldson and Doolittle, was getting a chance.

“Stephen is just a guy who can really play baseball,” said A’s hitting coach Darren Bush, a man Vogt cites as instrumental in making him a good big-league player. “Sometimes that takes a while to shine through. He’s had to earn it every time, at every level — and he always does.”

Clearly, Vogt doesn’t need to tout himself, even in comedic character. Plenty of others will speak for him.

“That guy has turned himself into one of the better catchers in the league,” said Twins catcher Kurt Suzuki, who worked with Vogt in Oakland late in the 2013 season. “When you have that and his offensive ability — well, it’s too bad he’s not one of the younger guys; he’d get more recognition. He definitely deserves it, but because he’s on the older side, people don’t talk about him. I’m hoping he makes the All-Star team because people should be noticing him.

“The way he’s playing and the way he’s catching, it’s hard not to compare him with Buster Posey. I mean, all past accolades aside, I’d put Vogt up there with anyone in the league, side by side right now.”

Another onetime A’s catcher, A.J. Hinch, now managing the AL West-leading Astros, has seen Vogt from the other dugout plenty this season.

“He’s one of the better offensive players in the league and the more you watch him, the more you appreciate how much he competes for the whole at-bat,” Hinch said. “He’s a tough out because he knows the strike zone. As much as he gets noticed offensively, he looks like he takes pride in handling the pitching staff, too.”

Said former A’s All-Star Yoenis Céspedes, now with Detroit: “Stephen has really gotten better as a big-league player. I can see him as an All-Star.”

Ex-A’s catcher John Jaso played with Vogt for both Oakland and Tampa Bay, including the minors. So he knows precisely how far Vogt has come.

“It’s awesome to see the power numbers he’s put up, plus he’s a great clubhouse guy, everyone gravitates toward him,” Jaso said. “He was sort of third-string phantom-ish catcher in the minor leagues and now look at him — he’s the guy.”

“I’m definitely a better player now than I was at any point in my life,” Vogt said. “I think if I’d made it to the big leagues at a more typical age, at 24 or 25, I don’t know if I’d have been ready. I’ve never been the player who stands out or everyone says, ‘My gosh, look at this guy!’ But I’m the one at the end of the season you look and you say, ‘Oh, he had a great year.’”

Susan Slusser is a San Francisco Chronicle staff writer. E-mail: sslusser@sfchronicle.com Twitter: @susanslusser