The winger has not featured since the 0-0 draw with Lincoln City last month and returned to Germany for tests and treatment on what was initially believed to be tonsillitis, but proved to be more problematic.
Dajaku is now back on Wearside and has been able to begin his recovery this week, but remains some way off full fitness.
"Leon is making progress, he's done a couple of days in the gym this week," Neil said.
"He's one that is going to be a little bit longer [in terms of his recovery], because he's not been able to do much of late.
"He's lost quite a bit of weight so we just need to get him back up to speed.
"That's where he's at."
Neil is hopeful that Dennis Cirkin will return to the squad, but Carl Winchester misses out as expected.
"With Carl [Winchester], as I said last week that's one where it's going to be weeks rather than days," Neil said.
"Dennis has been back out on the grass, so he's certainly closer."
Aiden McGeady is also in contention to feature.
"I think he gives us another attacking option and we all know what he is capable of doing," Neil said.
"Unfortunately for Aiden he's not been available for quite a long period of time now, but he's been training with us for a couple of weeks now, so we'll take a view and make a decision in terms of these games."