Pilkington is one of the world's largest glass makers.
The UK newspaper said the new bid involves the purchase of Pilkington shares at 165 pence each for a total of 2.2 bln pounds. The two companies are likely to agree on the deal by the end of the month, it said.
A spokesman at Nippon Sheet Glass, who asked not to be identified, declined to comment on the report.
Nippon Sheet first approached Pilkington last October, with an offer of 150 pence a share, but was rebuffed. It tried again at 158 pence/share a month later but was rejected again, the report said.
Nippon Sheet currently owns about 20 pct stake of Pilkington.
The newspaper said question marks about Nippon Sheet's ability to fund the deal have been raised as the firm plans to raise 570 mln pounds in debt to finance the purchase of stock it does not already own, the report said.