5:45pm: Jon Morosi of FOX Sports reports that Samardzija rejected a five-year offer that was worth slightly more than $85MM (Twitter link).

WEDNESDAY, 4:48pm: Jon Heyman of CBS Sports also hears that the Cubs have made a new five-year offer to Samardzjia, but he says the number is “definitely not in the vicinity” of Bailey’s $105MM guarantee and could be more in the $75-80MM range. Samardzija and his agents have not countered the offer, he adds.

Heyman notes that some Cubs people have spoken optimistically about trading Samardzija, only to sign him in a year and a half when he reaches the free agent market. Given Samardzija’s prioritization of winning, the Cubs would likely need to experience a drastic turnaround in 2015 to make that scenario plausible.

TUESDAY: Though most of the rumors surrounding Jeff Samardzija of late have understandably pertained to possible trade destinations, Gordon Wittenmyer of the Chicago Sun-Times reports that the Cubs are making a late push to extend their ace. Wittenmyer hears from multiple sources that the Cubs have offered Samardzija a new extension that would keep him in Chicago through 2019. While that contract length is the same as the previous five-year deals Chicago has offered, Wittenmyer says the new offer is for a higher guaranteed number than the previous $60-65MM figure that was proposed.

One source tells Wittenmyer that Samardzija would require something in the vicinity of the $17.5MM annual value that Homer Bailey received on his six-year, $105MM extension with the Reds. That deal, of course, essentially boiled down to a five-year, $95MM extension, as Bailey was already likely to earn about $10MM via arbitration in 2014.

Multiple sources also indicated to Wittenmyer that “at least” two teams, including the Blue Jays, have already had preliminary talks with the Cubs about Samardzija and exchanged potential names that could change hands. He adds that contenders that are looking for starting pitching this summer “still believe Samardzija is firmly on the market.”

A midseason extension for Samardzija certainly wouldn’t be unheard of; Cole Hamels was thought to be a trade candidate for a potentially rebuilding Phillies club in 2012, but Philadelphia instead inked him to a six-year, $144MM extension. Matt Cain signed a five-year extension that guaranteed him $112.5MM in new money shortly after the onset of the 2012 season, which could be a potential talking point in negotiations for Samardzija. That contract, however, was worked out entering Cain’s contract year, while Samardzija has one-and-a-half years of control remaining.

The Cubs are reportedly gauging the market value of Jason Hammel, Edwin Jackson and Jake Arrieta in addition to Samardzija — perhaps in an effort to assess what they can pull in via trade should they lock up their most valuable trade chip long-term rather than ship him elsewhere for what would surely be an impressive haul of prospects. Given Samardzija’s excellent season to date and the fact that he is controlled through 2015, it’s hard to envision the Cubs getting anything less than the package they received for two months of Matt Garza last summer. In my estimation, a team would have to top that package — C.J. Edwards, Mike Olt, Justin Grimm and Neil Ramirez — in order to pry Samardzija away from Chicago.

In 91 innings this season, Samardzija has pitched to a 2.77 ERA with 8.1 K/9, 2.6 BB/9 and a 50.2 percent ground-ball rate. Both the walk rate and ground-ball rate would represent the best full-season marks of his career, should he maintain them. Sabermetric ERA estimators love Samardzija’s work even more than usual, as FIP pegs him at 2.95, xFIP at 3.27 and SIERA at 3.39.