The Uruguayan was banned and fined 40,000 pounds (62,700 dollars) for racially abusing Manchester United's Patrice Evra during their Premier League match on October 15.
Liverpool have 14 days to appeal from the time they receive the full written judgement by the Independent Commission, which issued the ban under the authority of the Football Association.
But The Telegraph newspaper said that judgement may not come until mid-January, meaning Liverpool's appeal may not even be lodged until February.
"It is inconceivable an appeal will not follow given the strength of feeling on Merseyside," The Telegraph said. "However, Liverpool will then run the risk of seeing the ban extended even longer.
"The FA reserves the right to increase the penalty on the Uruguay striker should he request a new panel to convene to reassess the evidence."
Liverpool have given Suarez their unequivocal backing in the case, wearing T-shirts of support before Wednesday's game at Wigan and issuing a joint statement on their website.
Public opinion in Uruguay has rallied behind the striker. Fans, national team players and sports officials have shown their support for Suarez.
Uruguayan Sports Minister Hector Lescano said he planned to contact the player to show his support for a "disproportionate" penalty.
"The ruling has no solid arguments. Luis is a victim. I don't understand how a player like Evra can do this. He is violating every code in football," said Uruguay captain Diego Lugano, who plays for Paris Saint-Germain.
Uruguay defender Diego Godin noted the cultural differences between Britain and Uruguay, where he pointed out that the words "negro" and "negrito" are not considered offensive.