Allen has scored four goals in his last three games, which have helped the side to five points from their last three games. He scored both goals in the win over Sunderland, the equaliser at Old Trafford against Manchester United and opened the scoring in a draw against West Bromwich Albion.
Bowen is quoted by BBC Sport suggesting that the Welshman can continue his scoring form for a little while yet.
He said: "Why can't he get a double figure of goals? Without putting too much pressure on him, I don't see it ending too quickly.
"He'll keep doing the things that he's doing now right through the season."
His goalscoring form hasn't just been for his club as he has managed to score twice in the World Cup qualifiers for his country so far.
Allen's recent record for the Potters means he has matched his entire Premier League tally from his Liverpool days, who he joined Stoke from for £13 million in the summer.
He wasn't exactly renowned for his goals at Liverpool, or prior to that at Swansea and it must be pleasing for Stoke that they have discovered this scoring streak from Allen and in doing so they have added to their attacking options.
If Allen does achieve double figures this season then that would be an excellent contribution from any kind of midfielder for the season, and will certainly be regarded as a successful first season for the player.