The latter option would allow Manchin's temporary appointee to the seat, Carte Goodwin, to serve beyond November.
Manchin named Goodwin, his former chief counsel, on Friday under the premise that the 36-year-old would serve until a fall election. Goodwin will be sworn in Tuesday.
Byrd died June 28 with just over 30 months left in his term. The 92-year-old Democrat was history's longest-serving member of Congress, holding his Senate seat for more than a half-century.
Manchin has said it's highly likely he would run for the seat if there is an election. Manchin's probable candidacy has played a role in the special session debate, along with the special election's estimated $5.9 million cost.
The attorney general's opinion, meanwhile, has prompted some lawmakers to question the need for the legislation. A related, party-line debate centers on whether Rep. Shelley Moore Capito, the GOP's top prospect if there is an election, can run both for Byrd's seat and a sixth U.S. House term on the same ballot.
The education bills passed Sunday by the Senate include one that would redraw some of the in-school decision-making or advisory committees.
Another would require annual teacher evaluations. The remaining two would create pilot programs offering temporary pay boosts to educators and alternative settings for disruptive elementary and middle school students.