That would likely squeeze out one of the three running backs Tomsula took into Sunday's 32-17 loss to the Detroit Lions - Hayne, Harris and Kendall Gaskins.
Tomsula has been more reserved about Davis, telling reporters he would not rush Davis back to the field until he was ready.
Hayne was the surprise choice as the 49ers' starting running back in Detroit and carried most of the load, playing 35 of the team's 59 offensive snaps.
The former NRL star had his best game of the regular season with five receptions and nine carries for a combined 47 yards, including an 11-yard run to set up the 49ers' first touchdown.
Tomsula gave Hayne a lukewarm compliment in the post game press conference, telling reporters: "I thought he represented himself well."
The coach, who often goes out of his way to not personally criticise his players in front of the media, did single Hayne out for falling short of a first down marker on a key play late in the game.
"Jarryd just has to get to the sticks," Tomsula said. "He has to run the route to the sticks."
It was Tomsula who felt the heat of reporters' questions on Monday, with speculation he will be sacked after leading the team to an 11 loss, four win season.
Tomsula said he expects to be the 49ers' coach next season.
"Yeah, I'm the coach until someone tells me I'm not," Tomsula said.
-AAP