The Red Sox aren't "actively" searching for another starter, according to President of Baseball Operations Dave Dombrowski himself. However trades don't always happen out of nowhere: teams get in contact weeks or maybe even months in advance to gauge interest and price before actually attempting to complete a deal.
It sounds like that might be what the Red Sox and Padres are doing, as Boston contacted San Diego about a starting pitcher, but as far as we know, that pitcher was not James Shields. The reason that needs to be stated is because Shields is (and will continue to be) on the trade market as the Padres work their way further and further into rebuild mode under still-newish general manager, A.J. Preller.
ESPN Boston's Scott Lauber is the one who reported that the pitcher is unlikely to be Shields, given Boston's lack of interest in the fly ball hurler even before he struggled with keeping the ball in the park in 2015. Shields is good, and he'd likely help the 2016 Red Sox -- that home run issue is more likely to be fluke than feature -- but the concerns are more in regards to his long-term effectiveness: he has an opt-out after 2016, but given how year one of his deal went, there's a high-percentage chance he wouldn't take it and the Sox would be stuck holding the bill. Shields isn't getting any younger, and if his command falters, that's the end of his effectiveness.
So, if the Sox contacted the Padres about a pitcher, and the pitcher is not Shields, then who was it? This is more educated guess than reporting here, but back in July, before the trade deadline passed, the Red Sox were attempting to trade for Tyson Ross. The right-hander is under control through 2017, and he's the number two starter type that the Sox could very well end up needing in-season, should Rick Porcello prove ineffective, Eduardo Rodriguez struggle as a sophomore, or Clay Buchholz hit the DL after 100 innings. Dennis Lin of the San Diego-Union Tribune reports that Ross is among players considered trade candidates on the Padres, as well, so this just might all check out.
Ross is better at Petco than on the road, but let's not ignore just how good he still is away from that pitcher-friendly park. He's a strikeout pitcher who also induces tons of ground balls -- Ross posted 55, 57, and 62 percent grounder rates the last three years while averaging over a strikeout per inning in that stretch. This has allowed Ross to produce a 114 ERA+ over the last three seasons and 516 innings, and he's been almost a 200-inning arm in his first two full seasons as a starter -- Ross spent part of 2013 in the bullpen before shifting full-time to the rotation.
The 6-foot-6 right-hander limited opponents to a .248/.332/.353 line on the road since becoming a starter full-time, for an OPS of 685. That would be even lower if the Padres had been able to play defense even a little bit for him in 2015, but instead, they put together an infield where everyone except the first baseman was below-average for their position, and Ross' batting average on balls in play shot up to .320. Even with that hill to climb, Ross produced a 3.26 ERA and 112 ERA+ on the season.
So, we don't know if the pitcher the Sox contacted the Padres about was Ross, but he's the one who makes the most since. Andrew Cashner is a free agent at season's end, and he's an inferior version of Buchholz who hasn't had nearly as much success, and is coming off a rough 2015 -- the Sox don't need another question mark like that. Ross is the only sure thing in the Padres' rotation, and he's what would bring back the largest return. He would cost the Sox prospects, but Boston would get two years of a number two out of the deal, and be able to walk away when he's headed into his age-31 season to boot. That's a tempting thought even if the rotation were fully set.
If the rotation is in trouble come June or July, maybe the Sox open up more serious discussions with the Padres. For now, it sounds like they were just revisiting an old idea, maybe to see if San Diego is still interested in anyone in the Boston system after this winter's Craig Kimbrel trade that scored them Manuel Margot, Javier Guerra, and more. Ross wouldn't be quite that expensive, but he would still cost the Sox at least one major piece. That's probably why, more than anything, this is a discussion for another day.