Former First Minister Henry McLeish has discussed the potential solution in his role as chairman of the new board of governance for the region.
Glasgow has three colleges, but the regional board is responsible for the delivery of education across the city.
The suggestion came to light after The Herald yesterday highlighted concerns from students at Glasgow Kelvin College, in the north east of the city, with some saying they had been unable to enrol for courses, while others had to be sent home because no lecturers arrived to teach them.
Mr McLeish stressed discussions on an integrated system of recruitment had taken place before the current difficulties - but said this week's problems showed there was an "urgent need" for change.
He said: "Admissions and applications systems for students across the region are a priority for the new board.
"The matter was considered at its August meeting, where the board decided an analysis of the options available be carried out and the viability of a Glasgow-wide integrated system be explored by the colleges and partners."
His comments came after students from Glasgow Kelvin College took to social networking sites to complain after failing to get help from the college.
Civil engineering student Rory Nelson said: "It's our first day at Springburn campus. I can't express enough about my disappointment in the whole set-up." He added: "No info or help. Shambles."
Joanna Gordon said: "Absolute farce. No logins set up, so Tuesday night wasted and no lecturer turns up tonight. First week of college wasted. Sort it out please!"
After being instructed by the college to contact staff responsible for dealing with the issue, she added: "Spoke to him. He told me he was no longer head of department and couldn't help. Told me it was 'shocking'. That's four phone calls so far."
Gary Haldane said: "What a waste of time. Glasgow Kelvin College is a circus. Has been ever since the merger. Horrible."
Kayliegh Mullen said: "Went into college yesterday to be told my place on my course was given away. Turned down three other offers for that course!"
However, her situation has now been resolved.
Another student responded to a message from college officials to "enjoy her course" with the comment: "I will when I'm not being sent home because there is no one to teach us."
Following the complaints, the college issued a statement apologising for the situation.
A college spokeswoman said: "The college got off to a very busy start to the academic year, especially at our Springburn campus, where refurbishment and reconfiguration of space has impacted on the limits of class sizes.
"In a few cases, all those students offered a place have presented for enrolment. Creative timetabling has helped us as we schedule classes into rooms that can accommodate the number of students who opted for places at Glasgow Kelvin.
"There have been a few issues and concerns raised over adjustments to timetabling. However, our students' association has reported to the college management that due to action taken by college managers to address these, all issues have been resolved."
Glasgow Kelvin College was formed last year after the merger of John Wheatley, North Glasgow and Stow colleges as part of a Scotland-wide programme of re-organisation.