The Giallorossi failed to taste success in their opening three games this season but have since picked up three wins in four matches, and Luis Enrique wants his side to continue their momentum.
"We have overcome a difficult time," said the Spaniard, whose side bounced back from their 2-1 derby defeat at Lazio with a 1-0 triumph over Palermo to move up to sixth in the standings.
"We had problems at the start of the season but we are going in the right direction.
"Against Palermo, we played with intelligence and the team is improving.
"Now we must beat Genoa."
The odds seem to favour Genoa, who have beaten Roma in their last three meetings in Liguria.
Added to that is the fact that Genoa have not lost at home in Serie A this season.
However, Genoa coach Alberto Malesani is expecting a tough evening for his players.
"Roma will want to build on their win against Palermo and so we must look to limit the Giallorossi," he said.
"It will not be an easy task because they have great quality players but we are eager to continue to do well at home."
Malesani's Genoa lie two points behind Roma after last weekend's 2-2 draw at Juventus.
The hosts will be without suspended defender Kakha Kaladze as well as striker Ze Eduardo, who is ruled out for four weeks after having his appendix removed this week.
Roma are still without injured captain Francesco Totti while Bosnia-Herzegovina midfielder Miralem Pjanic is doubtful due to a muscular problem.