Executives have informed media agencies that in the week commencing 24 January average paid-for sales were 165,000 and reached a 180,000 record high on 27 January.
In the previous week, beginning on 17 January, paid-for sales were 138,000, according to executives.
The debut TV advertising for i launched on 16 January and will run for two months.
Executives have told media agencies that in the coming weeks the combined circulation of the i and The Independent will hit 360,000.
Executives have disclosed circulation figures to media agencies in an attempt to roughly double the amount they charge for advertising by bundling the two titles together and are promising media agencies a combined circulation of up to 340,000 a day.
According to Audit Bureau of Circulations (ABCs), the December circulation of The Independent was 175,002.
The i is expected to disclose its debut ABC figures for the month of February in March.