As reported in later editions of last night's Echo, the clubs agreed a price but Wallace rejected a move to Deepdale.
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Sports View podcast with Ian LawsHe has been on the transfer list since January, but wants to stay for the final year of his contract.
Sunderland had accepted a bid of around £1million for the former Celtic winger.
Preston chief Shaw said: "We made an offer for Ross Wallace, which was accepted by the Sunderland board.
"However, we have received word back that Ross wants to fight for his place in the Sunderland side in the hope of maintaining his status as a Premier League footballer, which we can fully understand.
"We will continue to back manager Alan Irvine throughout the summer as he continues to identify the right players to take Preston North End forward."
Wallace's decision means that Greg Halford remains the only summer departure from the Stadium of Light so far after he joined Sheffield United on a one-season loan on Wednesday.
Goalkeeper Marton Fulop continues to interest Stoke City, who hope to press ahead with a near £2million move for the Hungarian, who confirmed yesterday that the Potters were in talks with Sunderland.
The full article contains 225 words and appears in Sunderland Echo newspaper.