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Scherzer (back/arm) threw a 40-pitch live batting practice session Tuesday, Jeff Wilson of RangersToday.com reports.

Advice: It's the first time he's faced hitters since he had to be pulled off a rehab assignment in early May following a nerve problem with his throwing arm. Scherzer -- who initially went on the injured list as he recovered from offseason back surgery -- said after Tuesday's session that he's hoping his next step will be to make a rehab start. There remains no timetable for the 38-year-old return to the Rangers' rotation, but things are trending up. Rotowire.com Today, 1:44 pm

Yankees manager Aaron Boone said Tuesday that Cole (elbow) will require "at least a few" rehab starts before rejoining the major-league rotation, Chris Kirschner of The Athletic reports.

Advice: Cole will make his first rehab start Tuesday with Double-A Somerset and is slated to throw 40-to-50 pitches in that outing. If you bake in a 15-to-20 pitch increase in subsequent rehab starts, the righty would presumably require, at minimum, two additional outings after Tuesday's appearance. That would mean Cole won't rejoin the Yankees at least until late June, and it's possible it will take longer, depending on how things go and how he feels. Cole is working his way back from nerve irritation and edema in his right elbow. Rotowire.com Today, 1:33 pm

Eovaldi did not factor into the decision in Monday's 2-1 loss to the Tigers, allowing one run on three hits and no walks with seven strikeouts over 5.2 innings.

Advice: Eovaldi allowed a solo home run to Jake Rogers in the third inning but was otherwise fantastic, leaving the game in a 1-1 tie with two outs in the sixth. Eovaldi was pulled just shy of a quality start at 71 pitches, as he is getting eased back in after returning from the injured list (groin) May 28. Through nine starts, Eovaldi now owns a 2.70 ERA, 1.12 WHIP and 53:19 K:BB and will aim to continue building up his pitch count against the Giants this weekend. Rotowire.com Yesterday, 8:11 pm

Manager Rob Thomson said Monday that Suarez (hand) will play catch Tuesday and throw a bullpen session Wednesday before the Phillies decide on the left-hander's next step, Matt Gelb of The Athletic reports.

Advice: Suarez was forced out after just two innings in his most recent start against the Cardinals on Saturday, when he took a 106.1 mile-per-hour line drive off his pitching hand. X-rays cleared Suarez of any structural damage, but he's still dealing with some bruising and swelling that could present some difficulty for the southpaw in commanding his full arsenal. The upcoming bullpen session will represent an important test for Suarez in showing the Phillies' coaching and training staffs that the injury won't affect his pitching. At this stage, Thomson said that Suarez remains in play for his next turn through the rotation, which falls during the Phillies' two-game series with the Mets in London this weekend. Rotowire.com Yesterday, 1:40 pm