(CBS) In their never-ending chase to add a star, the Bulls have made an offer to the Timberwolves for All-Star forward Kevin Love, according to multiple reports.

The pieces of each report vary, though, so the full extent of the offer still seems unclear. The Bulls offered forwards Taj Gibson, Nikola Mirotic and Doug McDermott for Love, Chris Sheridan of Sheridan Hoops reported Wednesday morning. Chicago Sun-Times beat writer Joe Cowley confirmed that Gibson and McDermott were a part of the offer but added “the source could not confirm that” Mirotic was in the deal. However, there would be other assets for the Bulls to include in that situation, Cowley wrote.

Bulls general manager Gar Forman has also given a deadline to the Timberwolves to make a decision on Chicago’s offer because he doesn’t want to get in a bidding war with Cleveland, Cowley reported. That specific deadline isn’t known.

This news comes a day after ESPN.com reported that Chicago had made a “renewed push” for Love and was formulating a trade package around Gibson, Jimmy Butler and other assets. The inclusion of the sharp-shooting McDermott on his rookie contract would certainly sweeten the deal for Minnesota, which has also been involved with Cleveland in trade talks.

Because McDermott just signed his rookie contract Tuesday, the trade can’t be officially completed for another 29 days, per NBA rules.

Still, this could be an uphill climb for the Bulls so long as the Cavaliers are in the race. Top overall draft pick Andrew Wiggins remains the single best trade chip anyone’s shown a willingness to part with to date. Also, prior to his signing in Chicago, Mirotic’s camp sought assurances that he was in the long-term picture for the Bulls, the Chicago Tribune has reported.

Cleveland has reportedly been the favorite to acquire Love, who holds leverage in all this because he can become a free agent in summer 2015. Any team that trades for him will want assurances that he’ll re-sign on a long-term deal. The Cavaliers are reportedly forming a deal around Wiggins, 2013 top draft pick Anthony Bennett and a future first-round pick.

Speaking at a camp of his Tuesday, Gibson told reporters that Bulls hadn’t told him anything about being part of a trade.