He has up until a month to accept the deal.
Hernandez spent the first half of this season on loan at Leeds from Qatari club Al-Arabi but signed a short-term permanent contract with the Championship club in January.
The 23-year-old, who was also on the Baggies' radar 12 months ago, will likely be on his way out of Elland Road in the summer after refusing to play for the club in their final league outing.
Goalkeeper Ross Turnbull is one of six players to be released by Leeds.
Taylor can move on a free but because he is under 24, any club who signs him will have to pay United compensation.
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A product of the Leeds academy, Taylor slapped in a transfer request last summer too but Leeds stood firm in their determination to keep the player at the club despite the fear of him running down his contract.
Little progress has been made on reaching an agreement and Pulis says that West Brom are not prepared to go to a tribunal, claiming they do not want to pay over the odds for Taylor.
United's loanees - Kyle Bartley, Hadi Sacko, Matt Grimes, Mo Barrow and Alfonso Pedraza - are returning to their parent clubs but Leeds plan to pursue permanently deals for Bartley and Sacko.
New one-year deals have been offered to Eoghan Stokes and Tom Pearce and option have been taken up on the contracts of Conor Shaughnessy and Romario Vieira.
However, the West Yorkshire outfit announced on their official website that the full-back has been offered a two-year contract in line with EFL regulations.
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