Roberto Martinez's side have picked up 15 points from five matches to lead the section, five points ahead of third-placed Luxembourg, who are very much in qualification contention at this stage.
Match preview
Bruno Fernandes's 43rd-minute goal was enough for Portugal to beat Slovakia on Friday evening, with the result moving Martinez's team onto 15 points from their five matches in Group J.
Portugal, who have also scored 15 goals in the section and are yet to concede, are five points clear of second-placed Slovakia and also five ahead of Luxembourg in third on the same number of matches.
A Selecao das Quinas have qualified for the finals of each of the last seven European Championships, famously winning the competition in 2016, in addition to reaching the final in 2004.
Portugal's last-16 exit at Euro 2020 actually proved to be their worst performance in the finals of a European Championship, but they did improve to make the quarter-finals of the 2022 World Cup.
Martinez's side are seemingly breezing towards qualification for Euro 2024, and it would certainly not be a surprise to see them lift the trophy considering the quality in their squad.
Luxembourg, meanwhile, are bidding to qualify for the finals of a major tournament for the first time in their history, and it has been a strong qualification campaign thus far.
Indeed, the Red Lions have picked up 10 points from their five matches, courtesy of a record of three wins, one draw and one defeat, to sit third in the table, level on points with second-placed Slovakia.
This is already Luxembourg's joint-best European Championship qualification campaign in terms of points, and it would be some story if they were able to secure a spot in the finals of the competition.
Luc Holtz's side will enter this match off the back of a 3-1 victory over Iceland, which proved to be their third straight success in the section, also overcoming Liechtenstein and Bosnia-Herzegovina.
Luxembourg suffered a 6-0 loss to Portugal in the reverse match at the end of March, though, and they will be under no illusions when it comes to the size of the task facing them on Monday night.
Portugal Euro Champ Qualifying form:
W
W
W
W
W
Portugal form (all competitions):
L
W
W
W
W
W
Luxembourg Euro Champ Qualifying form:
D
L
W
W
W
Luxembourg form (all competitions):
D
L
L
W
W
W
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Team News
Luxembourg's recent improvement means that Portugal boss Martinez is unlikely to remove any of his big-hitters for this match, as it has the potential to be a tricky contest.
As a result, it would not be a surprise to see the same XI that took to the field for the game against Slovakia, with a certain Cristiano Ronaldo once again leading the line.
Ronaldo has scored five times since Martinez's introduction as head coach, with the 38-year-old very much still a vital player for his country at this stage of his career.
Pedro Neto, Goncalo Ramos, Joao Felix and Diogo Jota are among the attacking options hoping to come into the side, but it might be a case of same again for Martinez from the first whistle here.
Luxembourg, meanwhile, have not reported any injury problems from their 3-1 success over Iceland.
Danel Sinani is the leading goalscorer in the squad with 11, and he is once again expected to start in a deeper position for the visitors on Tuesday night.
Alessio Curci should lead the line for Luxembourg, with Yvandro Borges Sanches operating off the left, while Spartak Moscow's Christopher Martins is set to earn his 61st cap in midfield.
Portugal possible starting lineup:
Costa; Dalot, A Silva, Dias, Cancelo; Vitinha, Palhinha, Fernandes; B Silva, Ronaldo, Leao
Luxembourg possible starting lineup:
Moris; M Martins, Mahmutovic, Chanot, Pinto; Sinani, Barreiro, C Martins, Olesen, Sanches; Curci
We say: Portugal 2-0 Luxembourg
Luxembourg deserve huge credit for their recent performances and results in the section, but it is very difficult to back them to avoid defeat in this match. Portugal are looking strong under Martinez and have enough quality to comfortably make it six wins from their six games in Group J.