Bundesliga

Gerd Müller scored scored in 16 consecutive games in the 1969–70 season.

La Liga

Lionel Messi scored in 21 consecutive matches in the 2012–13 season.

Ligue 1

Vahid Halilhodžić (1984–85) and Zlatan Ibrahimović (2015–16) both scored in nine games in a row.

Premier League

Jamie Vardy holds record of scoring in 11 consecutive matches, he achieved this record in the 2015–16 season.

Serie A

Fabio Quagliarella and Gabriel Batistuta share the record of scoring in 11 consecutive games.

Sources

• Wikipedia articles of the individual players
• Wikipedia articles: Bundesliga records and statistics (current revision), Football records and statistics in Spain (current revision), Premier League records and statistics (current revision), Football records and statistics in Italy (current revision), List of Ligue 1 records and statistics (current revision)
• UEFA: Longest goalscoring runs in Europe's top leagues (Wayback Machine) (November 2015)
• BBC: Jamie Vardy breaks record for goals in consecutive games (Wayback Machine) (November 2015)
• Bleacher Report: Chronicling Records That Neymar and Kylian Mbappe Could Break This Season (Wayback Machine) (September 2017)
• The longest ever goalscoring runs in the major European leagues (Wayback Machine) (October 2017)