Monday's draw in Nyon paired the Turkish side against Brendan Rodgers' men, with the first leg set to be held at Anfield on February 19.
That match will represent a return to Merseyside for Ba, who on his last visit in April made the most of a slip by captain Steven Gerrard to help former club Chelsea win 2-0 and strike a blow to Liverpool's Premier League title hopes.
Liverpool have been well off the pace in the title race this season and suffered a disappointing Champions League exit after winning just one of their six group matches.
But striker Ba is adamant that Liverpool remain a dangerous threat and has called on Besiktas to make the most of playing away from home first.
"It's a difficult pairing. Liverpool are having some hard times now," he told UEFA's official website.
"They couldn't get the results they desired and things are not going well for them. Hard games are ahead of us.
"They are a team which try to strike fast and build up the game as quickly as possible.
"Their technical capacity is high and they are physically strong.
"If we can snatch a good result in the first leg, it will be an advantage to be playing the second leg at home."
