The French champions recorded a 3-0 win over Real Madrid in their Group A opener earlier this month, while Galatasaray started their campaign with a goalless draw at Club Brugge.
PSG returned to winning ways in Ligue 1 on Saturday afternoon with Neymar scoring the only goal in a 1-0 victory at Bordeaux. Thomas Tuchel's side have already lost twice in the league this season, but a total of 18 points is enough for the champions to top the table at this stage of the campaign.
The capital giants, meanwhile, beat Real Madrid 3-0 in their Group A opener on September 18. The likes of Edinson Cavani, Neymar and Kylian Mbappe were all absent for the home side, but Angel Di Maria scored a brace during what was a very impressive performance in the French capital.
PSG have actually lost on both of their two visits to Galatasaray - suffering a 1-0 defeat in the second group stage of the 2000-01 Champions League, in addition to a 4-2 loss in the 1996-97 UEFA Cup Winners' Cup.
This is the French side's eighth successive Champions League campaign - they have been knocked out in the round of 16 in each of the last three seasons, while they have not reached the semi-finals since 1995. It would be fair to say that the team are long overdue a serious challenge for this particular European trophy.
PSG have only won five of their last 12 Champions League matches, though, and have lost three of their four matches in Turkey. On paper, Tuchel's side are the favourites to collect all three points from Tuesday's affair, but the visitors are certain to be in for a very tough examination in Istanbul.
Galatasaray have made a modest start to their domestic campaign, picking up just nine points from their six matches to sit sixth in the table, five points behind leaders Alanyaspor. The Istanbul giants have won the last two Super Lig titles, though, and will still fancy their chances of landing the crown when all is said and done.
Fatih Terim's side will enter this match off the back of a goalless draw with Fenerbahce in the league at the weekend, meaning that they have shared the spoils in each of their last three fixtures.
The Turkish giants would have been looking to get their Champions League campaign off to a winning start away to Club Brugge on September 18, but the two teams played out a goalless draw in Belgium.
Galatasaray are actually without a win in their last eight European fixtures - they are unbeaten in their last six home matches against French clubs, though, and have lost just once against Ligue 1 visitors in Istanbul.
Last season, Aslanlar finished third in their Champions League group behind Porto and Schalke 04; a spot in the Europa League round of 32 followed, but they suffered a 2-1 aggregate defeat to Benfica to exit the competition.
Galatasaray form: DWWDDD
Paris Saint-Germain form: WWWWLW
Galatasaray will be without the services of Emre Akbaba as the midfielder recovers from a broken leg, but the home side did not suffer any fresh injuries against Fenerbahce at the weekend.
Mario Lemina, Steven N'Zonzi and Sofiane Feghouli are all likely to feature in midfield, while Radamel Falcao - a summer arrival from Monaco - is expected to lead the line against the French champions.
Younes Belhanda could also make the home side's XI having recovered from a broken jaw.
As for PSG, Mbappe made his return from a hamstring injury off the bench against Bordeaux at the weekend, and the France international is likely to feature in the starting XI on Tuesday night.
Neymar is also unavailable for the visitors as the Brazil international serves the second of his two-match suspension for insulting match officials following PSG's last-16 exit to Manchester United last season.
Galatasaray possible starting lineup: Muslera; Nagatomo, Marcao, Luyindama, Mariano; Babel, Lemina, N'Zonzi, Belhanda, Feghouli; Falcao
Paris Saint-Germain possible starting lineup: Navas; Meunier, Silva, Kimpembe, Bernat; Verratti, Marquinhos, Gueye; Sarabia, Mbappe, Di Maria
We say: Galatasaray 1-1 Paris Saint-Germain
For all of their talent, it is a big ask for PSG to win in Turkey on Tuesday night. The French champions have the credentials to record all three points, but we fancy a share of the spoils in Istanbul, which both managers would probably take if the result were offered ahead of kickoff.