"We've agreed terms but until he's signed his contract I don't think it's right to name any names," Bayliss told BBC Radio Cumbria.
"He's an attacking player who will make a big impression with the fans when we do sign him. The fans will be really happy with the signing."
While keeping the identity of the player under wraps, Bayliss has hinted that the player could have previously played for Barrow.
We'd love to have Wayne Curtis at the club but 99% that won't happen
Dave Bayliss
"The player himself is excited about it, he's agreed to come," he said. "His name probably won't come as a great big shock to some people."
Bayliss has effectively ruled out a move for Barrow-born striker Wayne Curtis, who was released by Morecambe this week after 12 years at Christie Park.
The 30-year-old joined the Shrimps from Barrow-based Holker Old Boys towards the end of the 1997/98 season and had a loan spell at Holker Street two years ago.
Bayliss said: "Unless there is a rich benefactor out there who can come along to help us with his wages that isn't going to happen.
"Our budget is not massive this year. We'd love to have Wayne Curtis at the club but 99% that won't happen."
Barrow have yet to add to their squad following the departures of several players following their FA Trophy final win against Stevenage earlier this month at Wembley.
Midfielder Carlos Logan, defender Gareth Jelleymen and forward Luke Powell have been released while highly-rated midfielder Andy Bond has turned down the offer of a new deal with the club.
Bayliss also revealed that goalkeeper Stuart Tomlinson is set to leave Holker Street.
"I don't think he'll come back," he said. "It's almost a done deal so we've basically discounted Stuart from Barrow now."
Source: BBC Sport
Source: BBC Sport