But the 27-year-old must first win his battle for a regular place at Upton Park following the arrival of Stewart Downing, another left winger eyeing an England recall.
Jarvis, who made his only England appearance against Ghana in 2011, does not want to be the forgotten man.
"Every team has competition for places and we have a very strong competition. Hopefully it will bring the best out of everyone and if we can get people watching here we can try and push for England places as well," he said.
"I would love to get back in there with England. I just have to make sure I play well for West Ham."
Allardyce is excited by the attacking and creative options he has assembled this season.
Hodgson confirmed that Morrison is on the England Under-21 radar after hearing positive reports about his impressive pre-season contribution for West Ham.
Allardyce believes this could be a breakthrough campaign for Morrison, who describes himself as a "changed man" from the teenager who found himself in trouble with the police and the Football Association.
- Sports & Recreation
- Sam Allardyce
- Stewart Downing
- Andy Carroll
- Roy Hodgson