And that tentative launching strikes U.S. Rep. Ed Bryant as something of a red flag.
The prospect of an Alexander race -- almost certainly vented by the two-time governor (and two-time presidential loser) himself -- was indicated in a Wall St. Journal brief on Friday and was picked up by the influential political website The Hotline.
The WSJ item reads in its entirety: "TENNESSEE WALTZ: Former governor and GOP presidential candidate Lamar Alexander ponders a 2002 Senate race if Fred Thompson retires. Continuing efforts to keep in touch with supporters for a possible 2004 rematch with Bush, Al Gore meets with fund-raisers and activists in San Francisco next week."
The item came in the immediate aftermath of Alexander's appearance last week, with former Vice President Al Gore, at a political seminar in Nashville.
At Friday night's local reception for nonagenerian John T. Williams at the home of Shelby County Mayor Jim Rout, Bryant referred to the matter.
"I wondered what he [Lamar] was doing giving all that free publicity to Al Gore. Now it seems obvious he had another motive," Bryant commented wryly.
The congressman has said a number of times that he will run for the Senate if Thompson, who seems increasingly reluctant to make another race, opts out. The WSJ item was the first indication that Alexander's thinking was moving in the same direction.
If the former governor turns out to be serious and is given the opportunity to run by means of a Thompson withdrawal, it will constitute something of an irony, in that Bryant was once thought to be pitted against his Tennessee colleague, 4th District Rep. Van Hilleary for either a Senate or a gubernatorial race.
Bryant defused that showdown in February with a statement that he would not run for governor. That, coupled with Thompson's renunciation of his own gubernatorial ambitions, in effect divided the stateside electoral turf between Bryant and Hilleary, with Bryant gaining de facto squatter's rights on a Senate bid.
Alexander's hint now complicates that scenario.