Lord Ahmed was sentenced in 2009 after pleading guilty to dangerous driving, having sent and received text messages in the build up to a fatal crash on the M1 near Sheffield on Christmas Day in 2007.
The final message was sent two minutes before his Jaguar struck the stationary car of 28-year-old Slovakian Martyn Gombar.
No causal link was made between the text messages and Mr Gombar's death, though.
The Times said it gained four separate Urdu-English translations to verify Lord Ahmed's comments during a television interview, which it said were thought to have been made in April last year during his visit to Pakistan. The newspaper claims the peer is seen saying:
I was charged with a traffic offence, for texting while driving. A traffic offence, dangerous driving, and it should have gone to the magistrates court.
My case became more critical because I went to Gaza to support Palestinians. My Jewish friends who own newspapers and TV channels opposed this.
More top news
Stars have vented their frustration over Sony's decision, with Rob Lowe comparing it to Neville Chamberlain caving in to Hitler.
Derby was unable to play with other dogs after being born with severely deformed front legs - but can now run freely.
The judge said the 14-year-old had been subject to a great injustice. He was executed for the murder of two little girls in 1944.