Bain is expected to join the Leith outfit on loan in January having been frozen out at Dens Park since October following a reported row with manager Neil McCann.
Parker discussed Bain’s imminent arrival after Oli Shaw pounced on an error by goalkeeper Jamie MacDonald midway through the first half to cancel out Kris Boyd’s second-minute opener at Easter Road.
“He has been in talks so hopefully (he will sign) because we have only one fit goalkeeper just now,” Parker said.
“So it will be competition for Ofir Marciano and that’s good. That’s what you need at this level. Ofir will need to be on his toes.”
Parker was left lamenting Hibs’ lack of cutting edge after having to settle for a draw.
Danny Swanson missed a great chance in the first half before John McGinn cracked a shot off the bar during what was largely a frustrating second period for the hosts.
He added: “We got off to a bad start but we got a bit of luck and I think we deserved that.
“We just couldn’t break them down but it wasn’t for the want of trying.
“Danny Swanson could have scored two, John McGinn has hit the bar. That’s the frustrating thing about it.
“Oli has done his job, he’s there to get anything if the keeper spills it and that’s what happened.
“We’re happy with where we are. We have dropped some points along the way but we can’t complain.
“We have just come up from the Championship and we’re in fourth. Let’s see what next year brings.”
Kilmarnock manager Steve Clarke, meanwhile, was delighted to end the calendar year in sixth place in the Ladbrokes Premiership but reckons a slow start under predecessor Lee McCulloch will haunt the Rugby Park side for the rest of the season.
Clarke, whose side have now gone six straight games unbeaten, said: “I don’t know if there’s been a transformation. I can only judge them since I came to the club.
“They’ve been great on the training pitch and they’ve taken on board every message we’ve given them and transferred that to the pitch.
“The results are there to be seen. You can tell by the run we’ve had. I think that’s only two defeats since I came to the club - that’s good.
“But as I said to the players, there’s still a long way to go and results today make sure you’re always looking over your shoulder in this league because it’s very difficult to move away from the bottom when you’ve only picked up three points from the first eight games.
“I think we’ll suffer for that for the rest of the season.”