According to ESPN's Stefano Fusaro, Minnesota called Houston with the offer Tuesday, but the Rockets won't part with Tucker.
ESPN's Adrian Wojnarowski reported Monday that the Timberwolves and Miami Heat were on the brink of a blockbuster deal involving Butler over the weekend. It fell apart, however.
Butler asked for a trade a few weeks ago and reportedly favored a deal to Miami because of the Heat's ability and willingness to sign him to a hefty extension.
Wojnarowski added that the Los Angeles Clippers, Brooklyn Nets and New York Knicks are among the other teams Butler has interest in joining.
Houston's ability to sign Butler to an extension is somewhat questionable given the big contracts guards James Harden and Chris Paul are already playing under.
Butler could be a rental in the Rockets' case as they attempt to push past the Golden State Warriors after losing to them in last season's Western Conference Finals in seven games.
The 29-year-old Butler is one of the NBA's best two-way players, and he is coming off a strong season that saw him average 22.2 points, 5.3 rebounds, 4.9 assists and 2.0 steals per game for the T-Wolves, who made the playoffs for the first time since 2003-04.
Gordon was named the 2016-17 NBA Sixth Man of the Year, and he was highly productive last season in primarily a bench role, averaging 18.0 points per contest.
Given small forward Trevor Ariza's free-agent departure, Gordon may move into a starting spot for Houston in 2017-18.
The Rockets signed Tucker last offseason, and he served as a part-time starter at power forward in 2017-18, averaging 6.1 points and 5.6 rebounds per game.
Tucker is a defensive stalwart who adds balance to Houston, which is best known for its high-octane offensive attack.
A Big Three of Harden, Paul and Butler would be a formidable foe for the Warriors in the Western Conference, but given Minnesota's reported asking price, it may not be worth it for the Rockets to deplete their depth so significantly.