Gascoigne joined Lazio from
Lazio's general manager Maurizio Manzini, who had the same position at the club in Gascoigne's time, said they would like the 45 year-old to attend the game in Rome.
Lazio and Tottenham have never played a competitive game before, and have been drawn together in Group J along with Greek side Panathinaikos and Maribor from Slovenia.
Manzini said: "Tottenham is a team Lazio knows very well, a great team with great traditions and we are very familiar with White Hart Lane starting from the time we had Paul Gascoigne.
"There is always a corner of Tottenham in our hearts. He is a mythical figure for Lazio fans and very popular in general in Italy.
"I remember the Atlanta ultras, who had a reputation for being really tough, opened an enormous banner with a picture of a huge bottle of beer saying 'This is for you Gazza'.
"I hope we will have the chance to see him in London and for sure we will invite him to the match in Rome."
Gascoigne has struggled to deal with alcohol problems since retirement but his agent said earlier this summer that he has embarked on a health drive.