Sheffield United have made an improved offer worth up to £20m for Oli McBurnie.
The Blades' latest move for striker McBurnie, 23, is understood to include a £17m initial fee with a further £3m in add-ons.
The Premier League new boys have made a number of bids for McBurnie and had their previous offer of £15m rejected a fortnight ago.
But the new bid is now being considered by Welsh side Swansea.
If successful, McBurnie would become Sheffield United's new record signing with his fee doubling the £10m spent on Lys Mousset last week.
United boss Chris Wilder is determined to sign a prolific striker this summer and wants to bring in either McBurnie or Brentford's Neal Maupay.
Scotland international McBurnie scored 24 times last season and Maupay scored 28.
