Sources told ESPN.com that Fesenko is on course to sign with the Bulls by week's end after working out for team officials this week.
Chicago has been searching for an established big man willing to come to training camp on a non-guaranteed deal because league rules prevent the hard-capped Bulls from handing out any guaranteed deals heading into the season.
But sources say the Bulls, if Fesenko has a strong camp, could well ask the burly Ukranian to wait until the Nov. 20 range, when Chicago would gain the ability to offer him a pro-rated veteran minimum deal.
Under the new collective bargaining agreement hatched last December, teams that use certain exceptions -- exceptions reserved for non-taxpaying teams -- have to live with a hard cap.
The Bulls brought on a hard cap when they signed guards Kirk Hinrich and Marco Belinelli this offseason using exceptions reserved for non-taxpayers. Their payroll, as a result, can't exceed the hard-cap limit of $74.307 million -- and it stands at $73.5 million.
Chicago is thus forbidden from signing veterans to guaranteed deals and so it will sign Fesenko, like veteran guard Nate Robinson before him, on a non-guaranteed basis.
After spending his first four seasons as a reserve center for the Utah Jazz, Fesenko, 25, was picked up midseason in 2011-12 by the Indiana Pacers. Fesenko, though, appeared in only three games in Indiana, averaging 2.7 points and 3.0 rebounds.
The massive 7-foot-1 center is a huge defensive presence but has struggled in the NBA to avoid foul trouble and develop his offensive game.
Yet, he continues to intrigue teams thanks to his considerable defensive potential. Fesenko's short stay with the Pacers was seen in some circles as the byproduct of an unfortunate 2011 offseason during which he sustained a knee injury playing for Ukraine's national team.