The White Hart Lane great is urging Spurs to relieve the growing burden on their playmaker by adding a proven marksman to their ranks before the season starts.
Allen, who scored a club record 49 goals for Spurs in the 1986-87 season, said: "Perhaps the biggest problem for Gareth will be to reproduce the same sort of form that he did last season.
"In particular, all those spectacular goals he scored. I am not sure he will be able to score as many spectacular ones next time, purely because people will now have ideas on to how to stop him.
"Getting a finisher, someone in the mould of their former striker Dimitar Berbatov, is something Tottenham have to address.
"They need to take some of that weight away from Gareth's shoulders. If they don't do it then the pressure on him will be massive."