If he meets certain conditions, Davies will be allowed to re-enroll in school and play basketball in 2011-12.
"There's a pretty long list of people that I'd like to thank who are helping me through this difficult time," Davies said in a statement released through BYU.
"It's been very hard emotionally, but thanks to the love and support of many, I'll be able to get through it. There's a plan in place, and I intend to follow through and return to BYU in the fall. I'm looking forward to coming back … and getting back on the court."
Jenkins said BYU officials "have every hope" that Davies will successfully navigate the course that has been set for his possible return to school.
"It is also our hope he will be able to suit up for the [2011-12] season," Jenkins said.
Davies, who attended Provo High School, missed BYU's final eight games this past season.
The Cougars went 5-3 without him, but two of those victories came in the NCAA Tournament against Wofford (74-66) and Gonzaga (89-67).
In BYU's first Sweet 16 appearance since 1981, the Cougars lost to Florida in overtime, 83-74.
If Davies is allowed to re-enroll in school and continue his collegiate basketball career, he will be a junior with two years of eligibility remaining.
Last season, he started 26 of 29 games and averaged 11.1 points and 6.2 rebounds.
If he returns, Davies will be a key member of coach Dave Rose's team, which is moving from the Mountain West Conference to the West Coast Conference next season.
The Cougars lose their top two scorers, Jimmer Fredette and Jackson Emery.
The consensus national Player of the Year, Fredette averaged 28.9 points. He is expected to be a first-round pick in the upcoming NBA Draft.
Emery averaged 12.5 points, and as a senior, became BYU's all-time leader in steals.
Brandon Davies, season by season
Season Games Min Pts Reb Ast
2010-11 29 24.9 11.1 6.2 1.5
2009-10 35 13.5 5.4 3.0 0.3