Billionaire Patrick Drahi is aiming to buy Vivendi's 20 percent stake in Numericable-SFR (NUME.PA) to strengthen his grip on France's No.2 telecoms group and prepare for a possible next round of industry consolidation.

Drahi's holding company Altice (ATCE.AS) and its subsidiary Numericable-SFR said on Wednesday they had offered Vivendi 3.9 billion euros ($4.5 billion), or 40 euros a share, for the media firm's stake.

While that is well below Numericable-SFR's current share price of over 50 euros, it is above the level at which Vivendi sold SFR to Numericable in November, which analysts say equated to around 33.30 euros.

A deal could allow Vivendi to boost a return of cash to shareholders or add to its warchest for acquisitions, while for Drahi it could clear the way for a long-mooted bid for smaller French rival Bouygues Telecom (BOUY.PA).

"From a Numericable-Altice perspective, this offer could be interpreted as organizing its finances in readiness for a Bouygues Telecom offer," said Jefferies analyst Jerry Dellis.

Telecoms firms across Europe have been striking deals, taking advantage of low interest rates to build up scale and seek cost savings in a saturated market.

Under Drahi's proposal, Numericable-SFR would pay half the offered sum to Vivendi in cash by buying back its shares, pending approval from shareholders in an April 30 vote.

Altice would pay the rest by April 7, 2016, plus interest.

Vivendi said its management board would examine the offer and its supervisory board, which next meets on Feb. 27, would decide on any action.

Vivendi sold telecoms group SFR to cable company Numericable for 13.37 billion euros in November, and was supposed to remain a minority shareholder for at least a year. It holds two board seats, and Altice had options to buy Vivendi's shares between the 19th and 43rd month after closing.

If it does accept, it would add to the cash pile Vivendi has accumulated from sales in the past two years as it exited telecoms and kept only its music and pay-TV businesses.

Led by chairman and largest shareholder Vincent Bollore, Vivendi wants to expand its existing media activities, possibly also via acquisitions.

Jefferies' Dellis estimates Vivendi had 8 billion euros net cash at the end of 2014, and said the Altice move would renew speculation of a larger return of cash to shareholders in 2015 than the 3.5 billion euros already planned.

"We remain skeptical that Vivendi shareholders will receive as much as some hope given management's presumed incentive to retain maximum capacity to re-engineer the rump media business and put it on a firmer growth footing," wrote Dellis.

In November, Altice CEO Dexter Goei said his company viewed itself as the "natural buyer" of Bouygues Telecom and was open to talks.

In recent days media reports have said Altice was preparing an offer for Bouygues, though Bouygues said no talks were underway.

Separately, Numericable-SFR published pro-forma results for 2014 with revenue coming in at 11.4 billion euros.

Adjusted earnings before interest, tax, depreciation and amortization (EBITDA) stood at 3.1 billion euros, while pro-forma capital expenditure was 1.8 billion euros.