Wallace returned to training with the first team this week and Driver isn't far behind him, raising hopes the talented pair will add to Jim Jefferies' options for the second half of the season.
But, with Ruben Palazuelos doing a great job as an auxiliary left back and David Templeton in flying form on the wing during a run of six straight wins, they're probably going to have to be patient in their bid to taste top-team action again.
"Lee trained in the gym with us the other morning and, if we could have organised a game next week, he could have played in that. He's not far away," said Hearts assistant manager Billy Brown.
"Andrew may also come back and train with us next week. The problem has been the weather, which has been keeping us inside.
"But they are coming on fine and aren't far away. They are going to be a good addition but, at the same time, it's not going to be easy for them to get back in the side."
For the first time in six games, Hearts had to change their starting XI for the midweek win at Motherwell after Eggert Jonsson and Ian Black were laid low by a bug.
Both players were expected to be back in contention for today's Tynecastle clash with Inverness Caledonian Thistle and Brown believes it would take something serious to rule out any player at the moment.
"You often find when things are going well, as they are at the moment, players don't want to miss games," he added.
"If you've ever been a player, you know the last thing you want to do is go out of a team when it is winning.
"If someone comes in, you can lose your place, so you will probably find that players will be desperate to play just now."
Hearts' recent run has rekindled memories of the 1997/98 season, when the Gorgie side not only lifted the Scottish Cup for the first time in 42 years but also pushed the Old Firm to the wire in the title race. "There's a similarity to 97-98 in that we are winning at the moment," acknowledged Brown.
"I don't think right now we have the team we had then. We may end up with that team and as the season goes on we may prove to be as good as that team. We are playing the same system that worked then and, if this team becomes as good – and we're on road to that – we will be very pleased.
"Things are going okay but we've got to keep our feet on the ground. We've got 32 points now – and the good thing about that is that I don't think we'll get relegated on that.
"Now it's a case of trying to kick on from there."
HEARTS will play city rivals Hibs at Tynecastle tomorrow (1.00pm kick-off) in a rescheduled fourth-round clash in the SFA Youth Cup.