Even with a club-record $118 million payroll projected for Opening Day, the Twins continue to prowl for pitching upgrades. They recently offered a two-year, $20 million contract to free agent right-hander Lance Lynn, according to a person with direct knowledge. That idea proved a non-starter as Lynn, the 30-year-old former all-star and three-time 15-game winner, opted to keep waiting for a suitable deal. Lynn has been working out in Jupiter, Fla., with noted trainer Eric Cressey, who also had recent Twins signee Logan Morrison and Rule 5 pick Tyler Kinley in his camp last month. Fellow right-handers Jake Arrieta and Alex Cobb also remain unsigned with Opening Day a little over three weeks away. Cobb is a former Tampa Bay Rays teammate of new Twins Logan Morrison and Jake Odorizzi, but the Twins don’t appear to be aggressively pursuing his services. “They’re still looking for another starter,” a rival scout said of the Twins. Ideally, that would come on a short-term commitment as the Twins, aside from a nine-figure offer to free agent right-hander Yu Darvish before he signed with the Cubs, have managed to keep all their additions to one- or two-year terms. They also made a run at veteran lefty C.C. Sabathia in December before the 37-year-old re-signed with the New York Yankees for one year at $10 million. Lower-cost free-agent starters still unsigned include Jeremy Hellickson, Ubaldo Jimenez, John Lackey, Clay Buchholz, Scott Feldman, Trevor Cahill, Jeff Locke and ex-Twins Ricky Nolasco, Matt Garza and R.A. Dickey. “You always want to balance cost and length and risk and everything associated with that,” Twins chief baseball officer Derek Falvey said last week. “While everyone’s focused on the 2018 roster, I’ve got my sheet with ’19, ’20, ’21, ’22 built out. I think as we think about future flexibility, we feel really good about where our team is headed moving forward.” The Twins have just $37.7 million committed to four players in 2019 — Phil Hughes, Addison Reed, Michael Pineda and Jason Castro — and no guaranteed money on the books for 2020.