But the rivalry is tempered by the fact that the respective managers – Eugene Taylor and Murray Balloch – are the best of friends, having previously been in charge of Edinburgh Athletic together.
"I have to thank Murray for giving me my introduction to coaching and management when he asked me to be his assistant some ten or twelve years ago," said Taylor. "Since we moved in different directions, Murray has the edge over me in wins directly against each other so I am hoping to redress that balance somewhat tomorrow."
Leith's outside chances of promotion were finally eroded in midweek when they lost 2-0 to Vale of Leithen and Taylor admitted: "There is no doubt that the better team won on the night. Vale came out of the traps quicker – maybe down to our travel problems and arriving late – but we gave ourselves a mountain to climb after conceding two early goals.
"However, under no circumstances would I criticise our players who have done brilliantly all season and Tuesday was just an off-night against a very good Vale side. I am sure that Vale will get promoted and probably win the league as well. Their manager, Rab Paget, is a real football man and has Vale well organised so good luck to them."
The last occasion that First Division Leith met Premier Division Tynecastle earlier in the season in the King Cup it resulted in a 3-0 win for Tynecastle.
"It was a very strange game because up until Tynecastle opened the scoring on the hour mark there was only going to be one winner – and that was Leith Athletic. We played Tynecastle off the park and then they scored two quick goals which knocked the stuffing out of us. I have only felt really disappointed with the results of two games this season and that was one of them along with the Vale this midweek.
"Tynecastle are a good, young side who are doing well this season. Murray is a superb manager and David Bingham is an excellent coach who I know plays the occasional game for them.
"This is the only competition we can win this season and it would be nice to take the scalp of a Premier Division side but we will have to be at our best."
Leith will be without their suspended striker Steven Radzynski who was sent off in midweek although Mark Duthie returns after suffering from a virus.
Tynecastle, who could yet secure a top-four finish in the Premier, are also looking to the League Cup to keep their season alive. "We have two league games left but if we don't win tomorrow then our season basically peters out," stressed Balloch.
"Obviously, we still want to finish as high up the league as possible after showing so much early promise.
"We have been forced to make quite a lot of changes during the season because of injuries and suspensions. We have a squad of 21 players but at one recent game we only had 14 available. Normally I would encourage boys from our Under-19 team to play but they have been doing well this season in various competitions and I would rather let them play there. Recently, we have not been hitting the target and scoring goals is our biggest problem.
"In our last meeting with Leith, nobody watching the game could have envisaged that we would win 3-0. Leith outfought and outplayed us but our goalkeeper John Gilbertson was outstanding and we got to half-time with a 0-0 scoreline. We were then a different side in the second half.
"Leith are a good, hard-working team and we will have to match them in every department.
"We have a few players – including Ross Elliott, Paul Devlin, Wayne Sproule and Robbie Arthur – who are all potential match-winners. Robbie is like a new signing for us because he has been out injured since September.
"He has given everybody a lift and he is a tremendous boost to the squad."
• THE action kicks off at the Civil Service Sports Ground at 2.30pm with the victors awaiting the winners of Lothian Thistle against Edinburgh City in the semi-final.