Since returning to the top-flight the club have added one player to last season's squad with the loan signing of Alex Cochrane from Brighton.
The only deals completed have been the loans of Ross Stewart and Josh Ginnelly being made permanent.
Regarding a signing this week, Neilson told Sky Sports: "Hopefully. It’s one we’ve been working on for a wee while now.”
The Hearts boss is keen to strengthen a few areas of the squad. Centre-back and forward have been mentioned previously, while the club have been linked with Everton midfielder Beni Baningime.
“We're still working on it,” Neilson said. “We’ve still got a number of positions we would like to strengthen.
"We’re hopeful of getting some done pretty soon.
Again, I’ll reiterate, it’s about bringing quality into the squad to make sure we push on."