Darrell Clarke gives George Dobson update as Sunderland look to seal signing number five
That offer is understood to be from Sunderland, who hope to make the energetic 21-year-old their fifth summer signing.
Dobson was not part of the Walsall squad that lost 5-1 to Aston Villa last night.
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Hide AdClarke confirmed that a fee had been agreed but said a deal was not over the line yet, with Sunderland now keen to agree personal terms.
"A fee has been agreed with a particular club," Clarke told the Express and Star.
"I'm not going to mention the club because it is not over the line yet.
"We'll see how things develop."
Manager Jack Ross believes the midfielder has significant potential and he already brings strong experience of the third tier.
After signing Reading striker Marc McNulty on a season-long loan, further outgoings are now likely before the transfer window shuts at the end of next month.