The Senegal international put an irreparable dent in Liverpool's Premier League title chances last year when he capitalised on a now-infamous Steven Gerrard slip to open the scoring in a 2-0 win for former club Chelsea.
Willian added the second for the London club in that April fixture, before Manchester City went on to beat Liverpool to the trophy.
Ba subsequently swapped Stamford Bridge for Turkey, but wants to come back to haunt Liverpool on his return to Merseyside.
"It is going to be a fun trip to Liverpool because I love playing in England," he said. "The atmosphere at Anfield is going to be amazing as it always is.
"I did my job against Liverpool last season, Gerrard was just unlucky, I did what I had to and hope to do the same this time around."
While Ba has fond memories of his last visit to Anfield, Besiktas as a club will be out to atone for their 8-0 drubbing the last time were at Liverpool - a match in which Gerrard found the net.
That fixture came in the group stage of the 2007-08 UEFA Champions League, when Liverpool made it all the way to the semi-finals, but a poor campaign this time around saw them parachuted into the Europa League.
Gerrard looks likely to miss Thursday's fixture with a hamstring problem, while Raheem Sterling (foot) is also doubtful.
Lazar Markovic, meanwhile, serves the first match of a four-game ban following his sending off in a 1-1 draw with Basel back in December.
Liverpool are unbeaten in five home matches against Turkish opposition, but are without a win in their last five European fixtures, and Philippe Coutinho is hoping to chip in with a few goals to help his side go as far as possible in the Europa League.
"I think the team has been playing well and that is important for Liverpool," he told the club's official website. "I work with my team-mates and, of course, I always want do a good job and improve, but I think the team has been playing well.
"I always work hard, but of course there are always things to improve and one of them is to score more goals.
"I have been working on that and in my position that is important. That is something I should improve."
Besiktas, whose coach Slaven Bilic denied reports linking him with a switch to Celtic in the near future this week, were dealt a blow on Sunday, when goalkeeper Tolga Zengin picked up a knee ligament injury.
