Bidders for Telecom Italia's (TIM) landline grid are preparing...

Bidders for Telecom Italia's (TIM) landline grid are preparing to raise their offers of around 20 billion euros ($22 billion) by between 1 and 2 billion euros ahead of a Tuesday deadline, three sources close to the matter told Reuters.

The sale of Italy's main fixed telecoms network pits U.S. fund KKR KKR.N , which is already an investor in TIM's TLIT.MI grid, against Italian state lender CDP, which has teamed up with infrastructure fund Macquarie (MQG) .

TIM is looking to sell its largest asset as CEO Pietro Labriola seeks to restructure the group, whose debt is rated as "junk" and which faces a steady revenue decline in its hyper-competitive home market.

TIM, which needs money to cut debt and relaunch its remaining services business, has asked both bidders to improve their initial offers by Tuesday. TIM's board is due to examine the offers at a May 4 meeting.

CDP, which owns 10% of TIM, initially offered some 18 billion euros ($20 billion) including debt for the grid which it plans to combine with that of Open Fiber, a rival fibre optic firm owned by CDP and Macquarie.

KKR bid 20 billion euros, including a 2 billion euro earn out, but both offers fall well short of a 31 billion euro price tag set by Vivendi VIV.PA , TIM's single biggest investor.

Vivendi, which has a 24% stake in TIM but has relinquished its board seats to have a freer hand in negotiations, has been urging directors to only assess bids that value the grid fairly and to put any decision to a qualified shareholders' vote.

If TIM decided to leave the decision in the hands of its board a legal battle could ensue, the sources said.

Piling further pressure on the board and Labriola, Vivendi is also planning not to back TIM's remuneration policy at a general meeting on Thursday, sources have said.

TIM is counting on the sale to cut its 25 billion euro debts, which Labriola has said is key to developing its industrial and strategic options. ($1 = 0.9108 euros)