Last week, after its parent company News International (NI) changed the terms of how much the supermarket is remunerated on individual copies sold.
NI had made the changes after lifting the cover price of the newspaper by 20p to £2.20.
Today both sides are claiming they have won in their head-to-head battle over the delisting of the Sunday Times.
Asda said the title is back on the shelves after News International had returned to the table with an "acceptable proposal".
But an NI executive told Media Week that it "sold to all retailers at the same price", and that it did not offer rates for individual supermarkets.
The mystery surrounding the return of the Sunday Times to Asda will not have escaped the attention of rival supermarkets Tesco, Sainsbury's and Morrisons.
If a deal has been struck with Asda then it would suggest the other supermarkets are losing out in comparison.
The Sunday Times was delisted by Asda's 260 stores after NI decided to keep 18.3p of the price increase for itself while offering retailers just 1.7p.
Asda said it should be receiving 5p, in line with the 25% share of the cover price that it was previously allocated. Following the price change, NI has reduced this proportion to 23.5%.
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