But the club will ask Newcastle United to fund up to half of the striker's wages next season.
With Newcastle boss Alan Pardew overseeing a major squad overhaul that has already seen Kevin Nolan join West Ham United, Smith has been deemed surplus to requirements at St James' Park.
The 30-year-old, who made just seven Premier League starts last season, is about to enter the final year of his contract on Tyneside.
He is well down the Magpies' midfield pecking order, and Mike Ashley is keen to move him on now rather than retain his services for another 12 months.
Smith is one of the highest-paid players on Newcastle's books, and is understood to earn around £55,000-a-week, a sum that represents an investment of almost £2.5m per year.
In order to save that sum, Ashley will allow the former England international to leave on a free transfer, and Simon Grayson is keen to bring him back to Elland Road.
Smith made more than 200 senior appearances for Leeds before leaving in an acrimonious £7m switch to Manchester United in May 2004.
However, Grayson is not in a position to pay anything like £55,000-a-week, and will require Newcastle to fund a significant portion of the midfielder's wages during what would otherwise be the final year of his Magpies contract.
The Leeds boss is yet to make a formal offer to Newcastle officials, but it is thought he will demand a payment of up to £30,000-a-week.
The alternative is that Smith writes off up to half of his pay packet for the next 12 months, and returns to West Yorkshire on a far less lucrative deal.
The Rothwell-born attacker still has strong links to his hometown club, but would be extremely unlikely to wave goodbye to more than £1m while simultaneously dropping down a level into the Championship.
At least one other Championship club has approached Newcastle for Smith's services, but their wage structure is understood to be even less flexible than Leeds.
With a switch to a Premier League club unlikely, Newcastle are therefore becoming increasingly resigned to a situation where they must either fund the whole of Smith's wages next season and keep him in their squad, or save a proportion of the payments by allowing him to move to a club that cannot afford to pay him in full.