Santana was at Baltimore's training complex on Monday, and he posed for a photo with young pitcher Eduardo Rodriguez, who sent it out on Instagram.
''In the past he was one of the best,'' Davis said. ''Hopefully he can regain his form and be a help for us. There are some things you can't coach and experience is one of those things, and he definitely brings that to the table.''
The left-hander threw for the Orioles and several other teams last week in Fort Myers, Florida.
Baltimore hasn't officially commented on a possible minor league deal for Santana, who last pitched in the majors in 2012 for the New York Mets. The two-time Cy Young Award winner had a second operation on his left shoulder last year.
''There are irons in the fire,'' manager Buck Showalter said. ''Certain things like that come to fruition at different times.''
Davis, the major league home run leader with 53, hit his first - and the Orioles' first - in their fourth game of the spring.
''It always feels good. I think the most important thing is seeing pitches early on,'' Davis said.
Bud Norris started for the Orioles and threw two shutout innings, allowing one, striking out two and walking one. Kevin Gausman followed and gave up a run on two hits in two innings. Gausman also struck out two and walked one.
Vance Worley threw three shutout innings for the Twins, giving up one hit and striking out one.
Minnesota scored seven runs in the ninth to break a 2-2 tie. The big hit was Wilkin Ramirez's three-run home run. Ramirez had four RBIs.
Twins: Worley had a forgettable 2013, his first with the Twins, going 1-5 with a 7.21 ERA.
''Last year, I was trying to put everything behind me. It was not what I wanted. It was not these guys traded for,'' Worley said. ''At this point, this is the guy that they got. I hope they're happy.''
Orioles: Norris is the leading candidate for Baltimore's fifth starter spot. Traded to the Orioles last July, Norris was happy with his outing.
''It went really well,'' Norris said. ''It's more about getting out there, getting back into competition and just feeling comfortable.''
Orioles: Outfielder Nolan Reimold was sent home after he complained of food poisoning. Orioles outfielder Henry Urrutia (sore right shoulder) reported some improvement.
Twins: catcher Josmil Pinto, who had been sidelined with a sore back, made his first start.
TAKING A TRIP
Suk-min Yoon will have to go to Canada to get a visa, but his trip has been delayed indefinitely. . Baltimore re-signed left-hander Chris Jones, who had been released last week to a minor league contract.