Free agency doesn't officially start until Friday, but the rumors are already in full force. According to Roch Kubatko of MASN Sports, "the Orioles like [Daniel Murphy] and could enter the bidding over the winter".
Murphy's postseason heroics likely changed the perception of his bat, and could result in the Mets extending him a qualifying offer. While Baltimore might not seem like a good fit for Murphy, as Jonathan Schoop appears to be their second baseman of the future, there are other options for him in the field.
In 2015, Murphy played 133 innings at first base, and 352 innings at third base. The latter doesn't seem like a viable option, as Manny Machado is firmly entrenched at third, but with Chris Davis hitting free agency, Murphy could be a decent back-up plan. Moving to the AL would also allow Murphy to DH from time to time, and provide some flexibility for the lineup.
Ultimately, the biggest road block to signing Murphy might be the qualifying offer. In recent years, as prospects have shown that they can have a dramatic impact on the big league club, teams have become more reluctant to forfeit their draft picks.
The Orioles didn't finish with one of the ten worst records in baseball this season, which means that their first round pick isn't protected. If they did sign Murphy, or any other player who's been extended a qualifying offer, Baltimore would likely have to wait until the compensation round to make their first selection in the amateur draft.
Other than the Orioles, the Yankees and Nationals could show interest in Murphy, as both teams could use an offensive upgrade in their infield.