The surprise approach by the London-based marketing services firm is likely to be worth 272.5p per share, valuing book and magazine print group St Ives at approximately 282m.
St Ives has agreed to receive a presentation from Tangent over the approach, but said that the proposed offer "significantly undervalues the company and its prospects".
The potential deal would have a cash element of 200p per share, with the remainder in new Tangent equity.
As PrintWeek went to press, St Ives' share price was at 248.7p, down 0.75p. Tangent's share price remained unchanged at 15.25p, its highest of the year.
Under Tangent's proposals, Michael Green, the former ITV chief who owns 45% of the firm, would be chairman of an enlarged board of directors. Charles Skinner, currently chief executive of tool hire company Brandon Hire and a former editor of PrintWeek sister title Management Today, would be chief executive.
Skinner said that, if Tangent's bid was successful, St Ives would be repositioned as a "third-party marketing and printing partner".
He said: "There is clear logic in combining St Ives with Tangent and repositioning the enlarged group away from being a pure printing business towards becoming a third-party marketing and printing partner for its expanded customer base."
Tangent Communications joint managing director Nicholas Green, Michael Green's nephew, said the reverse takeover would be a logical step.
He said: "In our view we see this as part of the industry's transition to the digital market. Digital communications is a growing sector and St Ives is a great company with a great client base."
He added that, if successful, Tangent would propose to spend more money on St Ives. He also said that the bid had "strong support from major financial institutions".
He said: "We have done a significant amount of work examining this opportunity. Our conversations with St Ives have been friendly."
St Ives has a turnover of 420m and was ranked 4th in last year's PrintWeek Top 500 league table. In contrast, Tangent Communications is ranked 297th with a turnover of 6.6m.
Tangent hit the acquisition trail back in July with the purchase of database management provider C360UK.
It was part of the company's strategy to move away from purely being a digital printer to a marketing communications group.
Close Brothers Corporate Finance is acting for Tangent as financial adviser. The board of St Ives is being advised by NM Rothschild & Sons. Under the terms of Tangent's proposal the combined group would have a net debt of around 160m and existing St Ives shareholders would hold 41% of the equity of the enlarged Tangent.
This week's announcement came after weeks of speculation over who could be behind the approach. A management buy-out led by chairman Miles Emley had been mooted in the national press.
St Ives
Turnover 420m
Staff 4,389
Sectors magazines, books, direct mail, point-of-sale, multimedia, commercial
Clients IPC Media, Virgin Group, Waterstone's, Penguin
Tangent Communications
Turnover 6.6m
Staff 103
Sectors direct mail, internet, email, SMS, point-of-sale
Clients Sainsbury's, Alpha Retail, Greene King, HarperCollins
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Ambitious Tangent is revealed as surprise bidder for St Ives
Digital innovator Tangent Communications could be in line to pull off a sensational takeover of St Ives, after it was revealed as the mystery bidder behind last month's approach.