The Dodgers have shown strong interest in trading for Rangers ace Yu Darvish , sources told MLB.com.

And that was before Dodgers icon Clayton Kershaw left Sunday's start with right lower back tightness.

The two developments -- Darvish's expected availability and the return of Kershaw's back issues -- will influence many conversations around the Major Leagues, as the sport enters the last full week before the July 31 non-waiver Trade Deadline.

The Dodgers view Darvish as an ideal fit for their rotation, sources say. He's a No. 1 starter capable of easing the postseason burden on Kershaw, who has made National League Division Series starts on short rest in each of the last four years.

Kershaw, 29, missed more than two months of last season with a lower back injury. The Dodgers have tried to lighten his workload when possible this year, giving the left-hander eight days between starts by slotting him fourth in the rotation coming out of the All-Star break.

As a right-hander, Darvish would bring a good contrast to the Dodgers' rotation. Including Sunday, the Dodgers have utilized a left-handed starter in 68.7 percent of their games this season (68 of 99). The Rangers haven't formally made Darvish available via trade but are expected to do so in the coming days.

The Dodgers scouted Darvish's most recent start, Friday against the Rays, and possess the farm system necessary to make a compelling offer. Sources say the Rangers are likely to ask the Dodgers for at least two of the following prospects: right-hander Walker Buehler, center fielder Alex Verdugo, second baseman Willie Calhoun and right-hander Yadier Alvarez.

Among that group, the Dodgers are most reluctant to part with Buehler, sources say. Buehler, who turns 23 this week, has a 3.44 ERA and 1.12 WHIP in 17 starts this season for three Dodgers affiliates. However, he allowed four earned runs without recording an out in his most recent game, his Triple-A debut on Thursday.

The Cubs, Yankees and Astros were among the other clubs that scouted Darvish's most recent start, sources say; all of those teams are pursuing rotation upgrades ahead of the Trade Deadline, as well.

Trade ticker

• Oakland's Sonny Gray has thrown at least six innings, and given up no more than two runs, in five consecutive starts -- his longest such streak since May 2015. He has a 1.62 ERA over that span. In short, his trade value is cresting.

The ideal timing led one rival executive to predict that the A's will attempt to trade Gray before his next scheduled start, Tuesday in Toronto. However, one source indicated Sunday that a trade involving Gray was not imminent.

• While the Brewers have been linked to Gray, among other starters, their most pressing need at the moment is offense. They are 3-7 since the All-Star break and have scored only 36 runs over that span, third fewest in the National League. Ryan Braun has started only two of Milwaukee's past five games, due to calf and wrist injuries that manager Craig Counsell acknowledged must be handled through periodic days off during the second half.

Perhaps as a result of the offensive struggles, the Brewers have checked into the possibility of acquiring Ian Kinsler from the Tigers, according to ESPN's Buster Olney. Brewers GM David Stearns could address multiple needs with a single trade, by acquiring some combination of Kinsler, starter Justin Verlander and left-handed reliever Justin Wilson from Detroit. (The Tigers almost certainly would need to include substantial cash if Verlander is involved, given his $28 million salary per season through 2019.)

In talking with the Brewers, Detroit GM Al Avila could conclude -- as White Sox counterpart Rick Hahn did before last week's trade with the Yankees -- that "bundling" players together opens up the possibility of acquiring premium prospects.

• Matt Adams smacked a game-tying home run off Kenley Jansen on Sunday, only the third homer the dominant Dodgers closer has allowed all season. It was the type of moment that makes Trade Deadline observers wonder where Adams will be dealt, during a season in which the Atlanta first baseman -- now 30 pounds lighter -- has posted an .893 OPS.

For now, at least, sources say the Braves aren't engaged in serious trade talks involving Adams. While it's very possible Adams will be dealt before Opening Day 2018 -- Freddie Freeman, after all, is the franchise first baseman -- the market conditions aren't ideal for Braves GM John Coppolella to move Adams now. Relatively few teams are actively looking to upgrade at first base, and two that could -- the Mariners and Angels -- haven't been showing interest in Adams, sources say.

Jon Paul Morosi is a national columnist for MLB.com.