Slew was given permission to talk with the Lancashire club less than three hours before the 11pm transfer deadline.
The deal was expected to be completed in time and would see the Blades receive an initial £1m and additional payments dependent on Slew’s success at Ewood Park.
Manager Danny Wilson has two players ready to fill the vacuum up front created by Slew’s departure with the planned arrival of Rangers duo Kyle Hutton and John Fleck, both 20.
Able to play either as strikers or attacking midfielders, they will join Sheffield United on season-long loans.
Only a month ago, Slew, 18, penned a new two-year deal with the Blades and had apparently resolved his future.
Fulham offered £500,000 for his services in the summer but the bid was rejected by the Blades.
Yet amid pressure to reduce the wage bill at Bramall Lane, the Blades always remained open to offers.
Blades striker Daniel Bogdanovic was also sold yesterday, joining Blackpool for a fee believed to be in the region of £100,000.
But the Blades rejected Blackpool’s advances for midfielder Stephen Quinn because the offer was not close enough to their £750,000 valuation.
Slew burst onto the first-team stage last season and also played a key role in the club’s march to the final of the FA Youth Cup.
Elsewhere in the county, it was a relatively quiet transfer deadline day, although new Bradford City manager Phil Parkinson took his tally of signings to five in less than three days since joining the club.
Parkinson’s deals included a permanent move for former Hull City goalkeeper Matt Duke and the loan signing of Hull winger Jamie Devitt.
Although Premier League clubs were again in a rush to beat the transfer deadline, there was far less pressure on clubs in the Football League to do business.
In just seven days, Football League clubs are permitted to re-enter the loan market and, at that stage, it will also be clearer who is surplus to requirements in the top flight.
Leeds United manager Simon Grayson has several loan targets in mind and will be armed with money from the estimated £2m sale of winger Max Gradel to French club Saint Etienne.
City’s new manager Parkinson is also expected to make use of the loan market in a bid to bring in a new striker.
Scott Parker’s anticipated switch to Tottenham was the major move of transfer deadline day as it approached its 11pm conclusion.
The 30-year-old England international handed in a formal transfer request at West Ham on Tuesday and has joined Spurs in a deal worth a reported £6m.
Tottenham manager Harry Redknapp had also hoped to sign Bolton defender Gary Cahill but admitted the deal could not be done. Surplus-to-requirements striker Peter Crouch was close to joining Stoke City in the wake of team-mate Wilson Palacios’s move to the Potteries, while right-back Alan Hutton was being targeted by both Fulham and Aston Villa.
The latter were also interested in a season-long loan move for Jermaine Jenas, while Redknapp said Croatia playmaker Luka Modric was staying after a £40m bid from Chelsea was turned down.
As well as Crouch, Stoke were chasing Birmingham striker Cameron Jerome and it is believed centre-back Scott Dann was in Blackburn for talks and a medical.
QPR were aiming to bring in Sunderland defender Anton Ferdinand to add to the completed capture of Manchester City winger Shaun Wright-Phillips.
Fellow City man Craig Bellamy left the Etihad Stadium, making a surprise return to Liverpool.
As well as offloading players, Manchester City completed the signing of Owen Hargreaves on a one-year deal following his release by Premier League champions and neighbours Manchester United.
Arsenal – mauled 8-2 at Old Trafford on Sunday – moved to bolster their defence, completing deals for defensive duo Per Mertesacker and Andre Santos from Werder Bremen and Fenerbahce respectively.
Gunners boss Arsene Wenger was also successful in his moves for two midfielders, Chelsea’s Yossi Benayoun and Everton’s Mikel Arteta.
Arsenal striker Nicklas Bendtner made a season-long move to Sunderland, Marouane Chamakh was linked with a loan move back to France and midfielder Henri Lansbury joined West Ham on a season-long deal.
Tottenham winger David Bentley joined the Hammers in a similar deal, while Liverpool’s Joe Cole agreed a season-long loan to French champions Lille.
The 29-year-old’s move gives the England international the chance of Champions League football again, while the Reds’ midfielder Christian Poulsen has departed to French club Evian.
Fulham completed the signing of former Juventus defender Zdenek Grygera on a free transfer and remained hopeful of tying up a £10.6m deal for Twente’s Costa Rica forward Brian Ruiz, although Newcastle made a late bid.
Chelsea made a last-gasp £12m raid on Liverpool to sign midfielder Raul Meireles with minutes of the transfer window remaining.
Recent Chelsea signing Ulises Davila joined Vitesse Arnhem for the season and Patrick van Aanholt headed for Wigan, who have also completed a deal for Celtic man Shaun Maloney.
Aston Villa said they had reached an agreement with Shamrock Rovers to sign Republic of Ireland Under-21 international defender Enda Stevens in January.