And why did the Dominican Republic native make such a request?
"Because this is a guy I've been following. It's exciting to see him," said Dotel to a pool reporter, after the White Sox contingency returned to its Baltimore hotel. "He's such a powerful man. I never met him before, and it's really, really neat to be around him.
"Just to be close to him and have that chance ... I saw the opportunity to ask for a hug. He said, 'Of course.' That was really nice of him."
Group shots were taken with President Obama, including one with everyone in the traveling party and one with the players. General manager Ken Williams presented President Obama with a black White Sox jersey with his name and the No. 1 on the back, and the president also received a dozen autographed baseballs, T-shirts and caps.
As for the tour, the White Sox group had the chance to see rooms not shown on the normal tour. Those rooms included the theater room where President Obama watched the Super Bowl.
"We got to see everything," Dotel said. "All we needed to see is where he lives. I'm telling you, it was great.
"He knows a lot about us. He noticed that we've been playing well lately. He's a big fan. I can tell he really enjoyed [the visit]."
President Obama stands as the most prominent White Sox fan in the world and is not shy about showing his support for the team. The president has been photographed coming back from workouts wearing his tried and true White Sox cap and has talked about his devotion to the South Siders in interviews.
It was then-Senator Obama who threw out the first pitch before Game 2 of the 2005 American League Championship Series at U.S. Cellular Field. And as the president has mentioned previously, the White Sox did not lose another postseason game during those particular playoffs.
Manager Ozzie Guillen was not present during Monday's visit, as he already had made plans to spend the day off with his family in Florida before the trip to the White House was officially arranged. Guillen might have the chance to meet President Obama if the president eventually is able to accept the White Sox offer to throw out a first pitch at any home game he chooses.
There's also the chance for another White House meeting if the White Sox can duplicate their historic effort from 2005. Dotel had previously been to the White House while playing for Houston, but never got to meet President George W. Bush.
The hug from President Obama on Monday more than fills that void.
"Nothing against President Bush, but this was a totally different feeling," Dotel said. "President Obama was there, and he knows the White Sox.
"I took the chance [by asking for a hug]. It was like I won the World Series. I was sweating and nervous. But it was a great moment, I'm telling you."