Fewer than 500 of the cheapest £10 tickets remain on sale for The Big One at St James' Park on Saturday March 24.
The 5.30pm Aviva Premiership kick-off takes place at the home of Newcastle United, and is preceded by a 3pm match between Newcastle University and Northumbria University.
Adult tickets start from just £10, but with ticket sales now past the 18,000 mark the club is down to the last 500 in this price category, all in the Gallowgate End.
Those wishing to book the cheapest tickets are urged to do so without delay, with the club confident of meeting its 20,000 target on the back of some strong recent performances.
Director of rugby Dean Richards said: "Playing an Aviva Premiership game at St James' Park is something the lads are really looking forward to, especially the local boys, many of whom are Newcastle United supporters.
"We have an Anglo-Welsh Cup semi-final this weekend and hopefully a final the following weekend before we start thinking about this game from a rugby standpoint, but it's great to hear the numbers of people buying tickets and the level of interest which is being generated around the fixture."
The Big One is already guaranteed to be Newcastle Falcons' largest ever home attendance, blowing away the crowd of 11,750 which watched their 20-15 victory over Bath in May 1998 at Gateshead International Stadium.
Following last weekend's victory at Gloucester the Falcons are currently fourth in the Aviva Premiership, with the top four going through to the play-offs, while the team are also well-placed to qualify for next season's European Champions Cup for the first time since 2004.
Tickets for The Big One at St James' Park are available by calling 0871 226 6060, clicking here, from Kingston Park in person or via the Newcastle United box office.