Derek Falvey, the Twins president of baseball operations, said in a recent MLB Network Radio interview that some Trade Deadline sellers are willing to bundle veterans in big deals in order to maximize the prospect return.

In fact, Falvey’s Twins are one candidate to do so.

Teams that have spoken with the Twins say the team could package another player with ace José Berríos in a trade before Friday’s 4 p.m. ET Deadline.

The most likely scenario involves coupling Berríos with a reliever such as left-hander Taylor Rogers, although Rogers’ early exit from Monday’s game due to a sprained middle finger on his pitching hand could result in another player replacing Rogers in that framework. Twins right-hander Michael Pineda, a free agent after this season, also is poised to be dealt after his quality start Monday against Detroit.

Berríos, 27, is the Twins’ top pitcher and most coveted trade candidate. There has been no apparent progress on an extension for the right-hander, and he is on track to become a free agent after the 2022 season. Sources say there’s a greater chance of Berríos being dealt this week than other controllable starters, such as Cincinnati’s Luis Castillo or Colorado’s Germán Márquez.

Many contenders in the market for starting pitchers also want to augment their bullpens, and it’s easier to justify parting with a top prospect in one trade that fulfills multiple needs. The Dodgers, Padres, Giants, Blue Jays and Phillies are among the teams known to be interested in the Twins’ available pitchers, sources say.

The Twins have long-term infield needs, which happens to be the strength of Toronto’s farm system. In addition to infielders Austin Martin and Jordan Groshans -- the Blue Jays’ Nos. 2 and 3 prospects, according to MLBPipeline.com -- No. 6 prospect Orelvis Martínez, 19, is posting a .979 OPS at Class A Dunedin while playing shortstop and third base.

Meanwhile, Twins outfielder Max Kepler has emerged in recent days as a legitimate trade candidate. The Yankees, starved for left-handed power, are among the teams with interest in Kepler, who hit 36 home runs in 2019. Kepler is under team control on a manageable contract through ‘24, which would aid the Yankees’ long-term efforts to comply with luxury-tax thresholds.

Three days before the Deadline, the chances of a Kepler trade are at least as high as those of a deal involving center fielder Byron Buxton.

Nats ready to deal?

The Nationals’ recent slide -- and shortstop Trea Turner’s availability on the trade market -- are major developments over the past several days. The Mariners are among the teams with interest in Turner, as Seattle general manager Jerry Dipoto reacts to an unexpected opportunity to reach the playoffs this year.

In trade discussions, Dipoto is focusing on players -- like Turner -- who are under control beyond 2021. While Turner plays the same position as J.P. Crawford, one of the Mariners’ best players this year, Turner has experience at two spots (center field and second base) where Seattle has lacked consistency this year.

The Turner and Whit Merrifield trade markets have considerable overlap; both players are non-rentals who offer premium baserunning and athleticism at multiple defensive positions.

Giants a fit?

While the Dodgers and Padres are more commonly mentioned in connection with Berríos, he’s a similarly strong fit with their division-rival Giants. San Francisco’s oft-celebrated success with starters on one-year contracts will have a downside this winter, when Kevin Gausman, Anthony DeSclafani, Aaron Sanchez and Alex Wood are all eligible for free agency. (The Giants also hold a club option on Johnny Cueto for 2022.) The arrival of Berríos this week would be a great start to their 2021-2022 offseason.

Worth noting

In talks for Berríos or a top rental starter like Max Scherzer, the Padres and Dodgers will be faced with an intriguing question: How comfortable are they -- and the acquiring team -- with the notion of having an injured starter as the centerpiece of a major trade? Padres left-hander Adrian Morejón and Dodgers right-hander Dustin May started games last postseason and are now rehabbing from Tommy John surgery.

The Padres and Yankees are mentioned as main suitors in the Joey Gallo trade conversations, but the Blue Jays also have checked in with the Rangers on his availability. At this point, a Gallo trade is more likely than a Gallo extension before the end of this week.