MINNEAPOLIS — David Price could make his first start of the season before the end of the month.

After weeks of purposely refusing to put a timeline on Price’s potential return, Boston Red Sox manager John Farrell outlined a scenario on Saturday that could put Price back on the mound in a big league game by a late May series in Chicago. That news could not come a moment too soon considering this week’s news that knuckleballer Steven Wright will undergo season-ending knee surgery Monday.

Price has been sidelined since late February with a left elbow injury, but he is scheduled to throw a four-inning simulated game on Tuesday in Milwaukee. If all goes well, Farrell said Price could make his first minor league rehab start about five days later. Triple-A Pawtucket is home on May 14 against Rochester.

According to Farrell, Price will make “more than a couple starts” in the minor leagues, which would represent the final step in a gradual spring training-style build-up of his arm strength. Price’s first minor league start will be four innings, and he will pitch every five days. If he increases his innings and pitch totals on May 19 and May 24, he could be slated to return in time to start one of the first two games against the Chicago White Sox.

Farrell has been encouraged by Price’s intensity in his previous two simulated games, which lasted for two and three innings, respectively.

“From the mindset that he’s generating, to be in full uniform, he’s taking it as a game day,” Farrell said. “And the adrenaline builds with that. His workdays have been very good.”

In Price’s absence, the Red Sox’s rotation has combined for a 4.17 ERA entering Saturday’s game against the Minnesota Twins. Ace lefty Chris Sale (1.38 ERA, 63 strikeouts in 45 ⅔ innings) has been nearly unhittable, while reigning Cy Young Award winner Rick Porcello has a 1.83 ERA in his last three starts and lefty Eduardo Rodriguez has allowed three runs or fewer in his past five starts. However, the Red Sox were dealt a blow with Wright’s injury, even while acknowledging the knuckleballer’s struggles this season (8.25 ERA).

Price’s return would allow the Red Sox to slot him into the rotation spot now occupied by right-hander Kyle Kendrick and would give them the three co-aces that they envisioned when spring training began.