Henderson, the English midfielder, is valued at £20m by the North East side, but Liverpool bid £13m last week and the two sides are now reported to be close to agreeing a deal for what could rise to £18.5m with clauses.
The 20 year old is believed to have expressed his desire to move to Liverpool, and a deal could be agreed before he travels away on Wednesday with the England Under-21 squad for the European Championship finals in Denmark.
Meanwhile, reports in Italy suggest Liverpool have agreed a fee to sign goalkeeper Doni, 31, from Roma as a back-up to Pepe Reina.
Liverpool continue to be linked with Blackburn defender Phil Jones, with The Mirror reporting the player has a £16m release clause and that the Reds are willing to meet that fee.
Another young English talent who is reportedly on the verge of moving to Merseyside is Ipswich striker Connor Whickham.
And finally, defender Danny Wilson is set for a season-loan return to Scottish side Glasgow Rangers, whom the Reds signed him from for £2m last year.