Barrow joint-boss Dave Bayliss has revealed the club have ended their interest in Andy Parkinson, but are keen to sign trialist Kelvin Lomax.
Lomax, 24, was involved in Saturday's 3-0 win at Colwyn Bay while Parkinson, 32, has ended his trial spell.
Bayliss told BBC Radio Cumbria: "We're not going to follow up on Parkinson as much as we'd like to, down to money.
"Kelvin is a lad we do want to sign, we'll see what's in the budget and hopefully get something done."
Parkinson was released by Accrington at the end of last season and has subsequently joined Aberystwyth Town, while Lomax is currently without a club after his exit from Shrewsbury in June.
Lomax's potential arrival at Holker Street would complete a busy summer of transfer activity for Barrow, in preparation for a fourth straight season of Blue Square Bet Premier football.
"You always want to strengthen it more, we'd like more, but we have a certain budget and we'll stick to it," Bayliss said.
"We're delighted with some of the players that we've signed, players like Gavin Skelton, Andy Ferrell, Richie Baker, Adam Quinn and Danny Hurst.
"There are some good players there, but the proof is in the pudding and we'll see how we get on next week and in the following games."