Ono and its private equity partners, are thought to be close to securing a deal to buy the fixed-line and cable assets of fellow Spanish telecom business Auna.
The proposed deal would be worth about €2.5bn ($3bn), including debt.
The proposed acquisition is central to the related but much larger sale of Auna's mobile phone unit, Amena.
A member of the Ono bidding team said: “We have the right engagement with the seller, our bid is being taken seriously, and we're close to signing something up.”
He said we have a “high degree of confidence”, adding he thought that an agreement on the fixed-line and cable assets could be announced next week.
Ono on Thursday refused to comment, but it is understood that the company's management is confident of sealing a deal soon.
However, there is no guarantee an agreement will be reached, and there remains a risk that Auna's large shareholders will abandon the auction if it is not satisfied with offers for both businesses.
Ono has joined forces with Providence and a trio of other private equity groups including Thomas H Lee, JPMorgan Partners and Quadrangle.
The private equity groups working with Ono have in recent days contacted investors to gauge interest in a possible debt finance package to fund the purchase of Auna's fixed-line and cable assets.
Auna, with a fibre-optic network covering nearly 10,000km in Madrid, Barcelona and much of Spain's north and south-east, completes the national footprint with Ono's 15,000km of infrastructure in the east and south-west of the country.
Driven by the massive task of taking on Telefónica, the former state-owned carrier, in fixed telephony and broadband internet, data and television, the two companies have been courting each other for more than a year.
Ono in November rebuffed a €2.4bn approach from Auna, deeming it too low.
Unlike Amena, with its strong brand and aggressive business plan, Auna's cable business has suffered from weak management, roll-out problems and a lack of identity.
By contrast, ebitda margins at the more agile Ono are more than twice that of Auna's.
In the first quarter this year, Ono reported a 16 per cent year-on-year rise in clients.
Together, the companies have a potential reach of more than 6m Spanish homes, or 40 per cent of the total.