Amid the recent speculation, Hill's voice was notably absent, and subsequent calls from PRWeek have gone unanswered, with his office saying he is reluctant to talk about the matter. It's not just his silence that distances Hill from Campbell; his very look is the antithesis of the Number 10 communicator's polished appearance.
Campbell's recent London Marathon run and his clean-shaven, sharp-suited look are in contrast to Hill's middle-aged spread, bald head and bushy moustache. The latter, as the once facially hirsute Peter Mandelson knows only too well, being a style entirely purged among other Labour PR men of the 1990s.
In fact, the nearest that wine expert Hill comes to matching Campbell's athletic image is in supporting Aston Villa, while Campbell cheers on a lesser team in claret and blue, Burnley FC.
Even his London postcode highlights the difference between the two. While Campbell lives in trendy Gospel Oak, Hill, described by those who know him as 'well-read', resides in Walthamstow, more famous for its dog track than its dinner parties.
Brought up in Birmingham, Hill was grammar-school educated before taking a place at Brasenose College, Oxford. Since then he has built up one of the most impressive pedigrees in the field of political communications.
Although not taking calls on the current speculation, he did manage to forward us his CV, to ensure accuracy from the safety of the shadows.
This charts his rise through the Labour Party machine, starting in the 1970s as a research assistant for Roy Hattersley, and then as his special adviser when Hattersley was secretary of state for prices and consumer protection.
He stayed with Hattersley in opposition as chief of staff until 1991 when he became the party's director of comms, a role that included overseeing the failed 1992 general election campaign.
Former party colleagues, including Hattersley, believe it would be a good move appointing Hill, who has considerable experience with Neil Kinnock in assisting a Labour leader under attack by the media.
Hattersley says: 'People trust him, he may say things brutally but that's part of his charm and style. If Hill tells you something then the likelihood is it's true. He's what Number 10 needs.'
Another former colleague, who declined to be named, agrees: 'He's good at briefing journalists and is very straight. One of the lessons to be learnt from the current situation is the need for briefings in front of the cameras. I see Hill more on the lines of the US President's spokesperson.'
Hill remained with Labour until 1998 as chief media spokesman, and achieved some kind of redemption for the 1992 campaign by overseeing 1997's highly successful effort, as well as the party's media strategy for Scottish and Welsh devolution.
After a quarter of a century in politics, he left the party machine in 1998 to join Chime Communications-owned Good Relations, returning briefly to advise on the 2001 election campaign.
Chime chairman Lord Bell says that if Hill does leave the firm, it would be 'a considerable loss', adding that 'he is an extremely talented communicator, good at giving strategic advice, wise and experienced'.
'They (Campbell and Hill) are like chalk and cheese. Campbell is an evangelical person, who sees himself as part of the Labour project. Hill looks at the long-term, he realises no one has a right to coverage and that there are good days and bad days,' Bell adds.
If Hill does move into the post, he will know better than most the kind of role he may be taking, as he is one of a handful of journalists and PROs to sit on the committee that is reviewing government communications.
This committee is due to report in the autumn, and is looking at, among other things, Campbell's role. Could it be that Hill is helping to prepare his own job description? His policy of silence, while honourable, will only fuel further gossip.
DAVID HILL THE STORY SO FAR
1976 Special adviser to secretary of state for prices and consumer
protection Roy Hattersley
1991 Director of communications, The Labour Party
1998 Director, Good Relations 2001 Election campaign adviser, The Labour
2003 Director of communications, Downing Street?