Taylor was taken to the hospital following a skirmish Tuesday evening outside of the university's student union building. Sources told the Lawrence Journal-World that players from the two teams were arguing as they entered and exited the building and punches were thrown.
It was one of two fights in 24 hours on the Kansas campus. The second fight took place early Wednesday.
Taylor was the only one injured in the first melee. None of the others involved was identified.
"Four weeks is on the high end," said Self, who was on a recruiting trip when the fight occurred. "The doctors told me three to four weeks."
A fight between KU football and basketball players broke out Tuesday night, and was reignited Wednesday morning.
Mangino said he was pleased with an afternoon meeting that took place with KU athletic director Lew Perkins that included the entire KU football and men's basketball teams.
"I think it went extremely well. I think the kids realized -- we're just talking about a few guys here -- that let their emotions get the best of them," Mangino said. "I think all parties left that meeting feeling pretty good, (but) feeling a little embarrassed, ready to get back on track."
Self said he did not have all of the details and did not know if there would be any disciplinary action taken against those involved.
"We're aware of reports of an incident and we are gathering facts as we speak," Kansas associate athletic director Jim Marchiony told the Journal-World.
As of late Wednesday afternoon, there had been no arrests or charges.
"We're hoping they get themselves together and act like adults, like they're supposed to be," campus police Capt. Schuyler Bailey said. "We're hoping that this is done."
In the second fight, which took place about 10 a.m. local time Wednesday on the other end of campus, witnesses reported some players hurling racial insults and a basketball player shoving a football player down some stairs.
The Kansas student newspaper said on its Web site that basketball players Marcus and Markieff Morris, Mario Little, Sherron Collins and Taylor were at the scene. The site also had a video of several basketball players, including Collins and the Morris twins, ushered into a van by associate athletic director Sean Lester.
Two football players, Chris Harris and all-Big 12 wide receiver Dezmon Briscoe, were seen talking to police.
Bailey said no police report had been issued on the second incident because no one had brought a complaint.
On his Facebook page, Taylor admitted he threw a punch.
"I got a dislocated finger ... from throwing a punch, so don't let the newspaper gas ya all up, aite," he posted after midnight, according to The Kansas City Star.
Taylor's earlier posts indicated there may have been some tension among the athletes on campus. On Tuesday morning he wrote, "keep my name out ya mouth for you get smacked in it." A half-hour later, a posting read, "never get outta character ... I'm always a G about it."
Later that afternoon, Taylor posted, "n-----s be muggin me ... you know I'm mugging back." The altercation occurred about two-and-a-half hours later, the Journal-World reported.
Kansas, the prohibitive preseason No. 1 team, is scheduled to begin its season on Oct. 16 with "Late Night at the Phog," its annual opening practice. The Jayhawks' first game is Nov. 13.
Taylor averaged 9.7 points and 3 assists as a freshman.
Athletic director Lew Perkins met with the football and basketball teams Wednesday, and representatives of each squad issued a statement in support of each other.
"We realize that over the past couple of days we've let a disagreement between a few guys grow bigger than it ever should have. We're embarrassed about that," the statement said. "Now we want everyone know that we have met and talked it out. We realize we're all Jayhawks. We're proud of what both teams have accomplished."
Dana O'Neil covers men's college basketball for ESPN.com. Information from The Associated Press was used in this report.