Inter president Massimo Moratti is reported to have met his directors yesterday and decided on increasing their original bid of £7.95m for the England star, according to The Sun.
New Inter coach Jose Mourinho is determined to land Lampard and the Italian giants hope a new move will open negotiations with Chelsea which could lead to the 30-year-old switching clubs.
Decision time: Chelsea midfielder Frank Lampard must make up his mind.
Moratti revealed he is looking at putting a back-up plan in place though if they are unsuccessful in their latest offer for Lampard.
'Lampard is the priority but naturally in cases like this I have been looking around for some time,' he said.
'If it is not possible to sign Lampard, we would take a player with the most similar characteristics.
'Lampard is a very serious lad. Certainly he is torn between having the pleasure of doing something new and a sense of duty towards his club.
'In the end it’s up to him to find a solution.'
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