The Little Britain comedian has repeatedly been linked to the ITV talent show and rumours of his involvement escalated following Michael McIntyre's decision to quit the panel last month.
However, The People reports that the BBC has attempted to snare Walliams away from ITV, apparently offering him "a fortune" to host the upcoming contest.
"The stations are at loggerheads," a source claimed. "David can't believe it and finds it very flattering. He thinks The Voice is one of the biggest events around the world and being the face of it is tempting.
"But David also loves Britain's Got Talent. He has a lot of experience and he knows about quality talent acts. David is more tempted by the BBC as Simon Cowell's shows seem more about in-fighting than talent these days. The Voice is with the panel turning their backs to judge contestants on their voices alone.
"But David would be head judge on Britain's Got Talent whereas he would just be presenting The Voice," said the source. "He just has to make a decision."
Jessie J is the only celebrity confirmed to judge The Voice thus far, while Tom Jones and will.i.am are said to be in talks.
Digital Spy readers recently named Paul O'Grady as their dream Britain's Got Talent judge.