The newly-promoted Reds have already lengthened the deals of joint top-scorer Woodrow and 21-year-old winger Jacob Brown until 2022, while they have converted midfielder Mike Bahre’s loan into a permanent deal and took their option to extend right-back Dimitri Cavare’s deal into a third year.
They are hoping to finalise a deal for long-term coach Dale Tonge as assistant to head coach Daniel Stendel following their success as a partnership in the first half of 2019.
Extensions are thought to have been put to central midfielder Cameron McGeehan, winger Mamadou Thiam and star centre-backs Liam Lindsay and Ethan Pinnock.
All of that quartet started regularly during the promotion season and have a year remaining on their deals. The Reds are hopeful of making progress with some of them in the coming weeks but the likes of Lindsay and Pinnock are known to be targets for other clubs.
Kieffer Moore, who netted 19 goals last season, is understood to be on the radar of Barnsley’s Championship rivals Bristol City. Sources in the South West have revealed that the Robins, managed by former Reds head coach Lee Johnson, are considering a move for the tall targetman.
City have money to spend after selling full-back Lloyd Kelly to Premier League Bournemouth for £13million earlier this month.Moore, 26, is contracted at Oakwell until 2021 and it is likely to take a multi-million bid to tempt the Reds to part with one of their key players.
Should he sign Moore, it would not be the first time Johnson has poached a Barnsley promotion hero as he brought Josh Brownhill to Bristol 48 hours after the midfielder helped the Reds win the 2016 play-off final. Moore is one of only two senior strikers at Oakwell, along with Woodrow who joined him on 19 goals in all competitions last season.
Davies, the goalkeeper and captain, is still expected to move to Stoke City on a free transfer with his contract now expiring. The Reds offered him a new deal earlier this month but he is expected to reject it to move to the Potteries.
Moore and Davies, both 26, were the two oldest players at the club last season so their exits would make one of the youngest squads in the EFL even younger.
They are both currently with the Wales national team squad and will be until mid-June as they visit Croatia and Hungary in qualifying games for the 2020 European Championships.
Davies’ exit would leave them needing another goalkeeper, with only 21-year-old Jack Walton – who has played six league games – and untested teenager Jake Greatorex currently contracted.
Wales international winger Ryan Hedges has also been offered a new deal as have under 23s Jordan Barnett, Amir Berkovits, Sam Fielding and Will Smith as well as under 18s Tommy Willard, Harry Gagen, Henry Kendrick and Jasper Moon.
Romal Palmer, a 20-year-old central midfielder who was loaned out to non-league Darlington last season, has signed a new one-year deal.
Barnsley will have until Thursday, August 8 to make incoming permanent and loan signings, with the Championship season due to begin on August 3. The 2018/19 fixtures are set to be released on June 20, with the players due back at Oakwell for pre-season training the following week.