The Star understands Harriet is one of the club’s summer targets, with George Moncur, Adam Hammill and Aidy White having already signed contracts at Oakwell.
But the Addicks have turned down the Reds’ initial offer to sign Harriet, a 22-year-old highly-rated winger.
Harriet spent the first half of last season on loan at Colchester United, scoring seven goals in 24 appearances for the U’s.
His impressive displays earnt a recall to The Valley and he went on to score three goals in the Championship to further enhance his reputation.
Harriet is out of contract after his three-year deal expired last month. It is unknown whether the Addicks have offered the winger a new deal, but even if they have the Reds could still sign the player because he is under 24 and compensation could figure in any potential deal.
The Star also understands the Reds are looking at raising their offer for sought-after Walsall striker Tom Bradshaw.
The Reds have already had a bid for the player rejected and the Saddlers are believed to want as much as £750,000 for a player who netted 20 goals last season.
A number of other clubs are reportedly chasing the 23-year-old’s signature, but Walsall are happy to sell if the price is right.
New Grimsby Town signing Rhys Browne has revealed he spoke to Barnsley about a potential move to Oakwell this summer.
Winger Browne said: “I spoke to a few clubs in January and them there was Barnsley and Eastleigh this summer, but this [joining Grimsby] was the option that stood out for me.”
The Reds are continuing their pursuit of out-of-contract Plymouth Argyle defender Curtis Nelson.
A big has been lodged with the Pilgrims who have offered the player a new deal to stay at Home Park.
Meanwhile, the Reds have been handed a tough opening month in their first season back in the Championship since 2014.
Paul Heckingbottom’s promoted side are away to Ipswich Town on the opening weekend of the new campaign on Saturday 6 August, followed by testing fixtures at home to Derby County and Queen’s Park Rangers, then Huddersfield Town and Rotherham later in the month.
The Reds have been drawn at home to League One Northampton Town in the first round of the EFL Cup on Tuesday 9 August.