The 29-year-old was an unused substitute during Saturday's 4-1 defeat at Inverness after recovering from the hamstring injury that has kept him out since August. Central midfielder Iain Davidson is suspended for the Boxing Day visit of Clydesdale Bank Premier League leaders Celtic, but Smith will not throw O'Donnell straight back into the starting line-up.
"He's not quite ready to start the game but I think it's great to have him back on the bench and available," Smith said.
"He's not actually match fit but it's good to see him recovered from what he's had and available for the bench at least.
"We'll see how he's feeling. It's not an easy thing and we will just see how he is between now and Wednesday."
Dundee have Aberdeen at home and St Johnstone away after hosting the champions and goalkeeper Rab Douglas believes it will be a crucial period.
Douglas, who played alongside Celtic manager Neil Lennon at Parkhead, said: "They are massive, we have Aberdeen and Celtic and it will be big crowds. It will be good to see Dens full.
"We have got to believe. The Inverness game is history. We have to look forward to the next game and cut out the basic mistakes.
"After a game where you lose and you are still in the game, you want a game quick, and that's what we have got.
"I have been at Celtic, boys almost seem to try harder against the Old Firm and then maybe lose against a lower team the following week."