Georgia Tech also might have to outbid the other schools for Johnson's services.
Johnson, who already has had talks with SMU and Duke this week, might be the top outside candidate on Georgia Tech's list. Johnson was believed to be interviewing with Georgia Tech officials Wednesday.
There were indications Wednesday that the interest Johnson has received from other schools could force Georgia Tech to make a quick decision on a possible offer.
If Georgia Tech makes an offer to Johnson, the school might have to dig deep into its finances to match possible offers from Duke and SMU.
The Annapolis Capital has reported Duke might offer up to $2 million to Johnson. The Dallas Morning News has reported Southern Methodist will match or top Johnson's current $1.5 million deal with Navy.
The Dallas paper reported there was no agreement between Johnson and SMU after the coach was flown into Dallas on Monday night for a tour of the campus and facilities.
Johnson is represented by Atlanta attorney Jack Reale, who did not immediately return phone and e-mail messages Wednesday.
Georgia Tech already has to pay Chan Gailey, who was fired after a 7-5 regular season, about $4 million.
Defensive coach Jon Tenuta will serve as interim head coach for Georgia Tech's Humanitarian Bowl game against Fresno State on Dec. 31.
Georgia Tech athletic director Dan Radakovich has said Tenuta will be considered for the full-time position.
Johnson, the former Georgia Southern coach, has attracted interest because of his strong record at Navy.
Johnson took over a Navy program that was 1-10 in 2001. Navy is 8-4 and will play Utah in the Poinsettia Bowl on Dec. 20 in San Diego. Johnson has taken Navy to five consecutive bowls.
"As any other human being would, if someone calls and asks to talk to me about another job, I may listen," Johnson said recently.
"But it would take a special deal for me to leave."