According to reports from Manchester United Evening News, a discussion has taken place between the officials of the two clubs but nothing has been finalised yet.
All the big teams generally play the International Champions Cup, a pre-season trophy held in the USA every year.
The schedule of the tournament will be released next month in New York. Accordingly, the dates of the tournament will be finalised.
Barcelona had played against Liverpool last season and were humiliated 0-4.
The Catalan giants have had a forgettable season this time as they are virtually out of the UEFA Champions League and likely to lose out on in the race for La Liga title against rivals Real Madrid.
Manchester United, on the other hand, won their maiden trophy of the season, the EFL Cup. They are very much in the race to finish among the top four in the English Premier League and have qualified for quarter-finals of FA Cup and round of 16 of Europa League.
In 2015, Manchester United had faced Barcelona in the International Champions Cup which the Red Devils had won 3-1.