Juve will surely place greater significance on their weekend Serie A meeting with high-flying Roma, while the visitors have a big relegation clash against basement club Benevento which is likely to occupy their attention.
As such, both managers are likely to make changes for the midweek cup clash, but even with a much-changed starting eleven the hosts should be too strong for a side they comfortably beat both home and away in the league last season.
Genoa have not enjoyed recent trips to Turin, with the north-western side losing each of their last four away matches against Juve without managing to find the back of the net.
All of those defeats have come in Serie A, but backing that sequence to continue in the cup is tempting as Max Allegri's side are offered at 10/11 (1.91) to win to nil.
While Genoa have been stronger on the road than at home this season, they are unlikely to be strong enough to cause the hosts any real problems - especially given the likelihood of them playing a second string side.
In the previous round at home to Crotone, Genoa manager Davide Ballardini made a number of changes to his starting eleven and players are likely to be rested once more, meaning that the hosts have every chance of extending to five their run of consecutive home wins over the Ligurian outfit.
Also worthy of consideration is backing under 2.5 goals at 21/20 (2.05), with this bet paying out in three of Juve's last four matches - as well as in seven of Genoa's last eight fixtures - as on a cold midweek cup evening in northern Italy, with neither side prioritizing the game, goals could well be hard to come by.