The boost, which is a 5% hike on the £149m it currently receives, is well above the rate of inflation, while reports indicate that the figure could increase further if it would ensure Airey remaining at the broadcaster.
Airey is understood to have been offered £3m to head up ITV, which has a £775m annual programming budget.
According to reports, she is demanding a double-digit increase in Channel 5's budget as well as a salary increase from Channel 5 shareholders RTL Group and United Business Media, if she is to stay.
It is also thought that she is hesitating about leaving the channel, which rebrands as Five on September 16, because of share options she holds in the UK's fifth broadcaster, which could convert to millions of pounds if the station were sold or floated.
The channel could be bought by BSkyB if the government relaxes media-ownership laws preventing Rupert Murdoch from owning a UK terrestrial broadcaster, apart from ITV.
Channel 5 has already been given a programming budget increase this year. RTL and United, which own 65% and 35% of the channel respectively, awarded the channel £3m as a reward for increasing its advertising and audience share.
However, its £149m budget still pales into insignificance against ITV, which received a £25m increase earlier in the year.
Airey is not expected to make a decision about moving to ITV for a couple of weeks because she is on a three-week holiday.
At the weekend, it was reported that former DJ and TV presenter Chris Evans was in talks to buy United Business Media's 35% stake in Channel 5.
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