Sessions said he was interested in speaking with Trump about the race but the opportunity "hasn't been provided at the moment."
Among those seeking the GOP nomination to take on Democratic incumbent Doug Jones is former college football coach Tommy Tuberville and GOP Rep. Bradley Byrne.
Trump has not signaled if he has a favorite among the other GOP hopefuls, but has made reference recently in off-the-cuff public remarks to "the coach."
Trump will be in Alabama on Saturday when he attends the biggest college football game of the year, No. 2 Louisiana State vs. No. 3 Alabama in Tuscaloosa.
Meantime, Trump said he would be happy if former New York Mayor Michael Bloomberg launches a bid for the Democratic presidential nomination. Bloomberg signaled Thursday he is preparing to possibly do just that.
"He's not going to do well, but I think he's going to hurt Biden, actually," Trump declared over the loud hum of Marine One's engines, referring to former Vice President Joe Biden. "There's nobody I'd rather run against than 'Little Michael.'"
That was a reference to Bloomberg casting himself as a political moderate and his potential impact on a three-way 2020 general election if the former VP is the Democratic nominee. Biden has tried to claim the moderate ground in the Democratic primary as he tries to defeat more liberal Democrats, like Sens. Elizabeth Warren and Bernie Sanders.
Trump signaled he will not allow Acting White House Chief of Staff Mick Mulvaney to testify before the House impeachment committees, which issued a subpoena that the former GOP congressman has ignored.
"I don't want to give credibility to a corrupt witch hunt," Trump said, before sending a mixed message. "I'd love to have Mick go up, frankly. ... I think he'd do great."
The president claimed he would prefer to allow "all" White House and administration officials testify but "I have to listen to the lawyers to a certain extent -- not always."