Sheringham was offered a part-time coaching role with the forwards at West Ham this summer, and the former Spurs and Manchester United star has thrived in the position so far.
Saturday's 3-1 win against Liverpool was West Ham's best display of the campaign so far, and Sam Allardyce's side are looking a lot stronger than they did 12 months ago.
They have scored nine goals in five games this season, picking up seven points in the process. At the same stage last season, they had scored just four times and were two points worse off.
Sheringham's impact as the striking coach could be a large factor behind their improvements in front of goal, and the 48-year-old is eying up a managerial job in the future.
"I've done my bit of coaching and I'm enjoying that," talkSPORT quotes him as saying. "Obviously I've got a lot to learn, because I've only been in there three months, but it makes me think that I want to have a go [at management] and see where it takes me.
"I was out of the game for six years and was quite happy, enjoying my life. But I thought to myself I better take my coaching badges, so I signed up to do them last summer, and then Sam phoned me and asked if I fancied a job doing the strikers.
"Sam been fantastic for me, he lets me into all the meetings and tells me what goes on and what he has to get on with, other than football things. I've got every respect for him and I enjoy being around the way his man-management is. You can tell the lads love playing for him."
Sheringham has been impressed with the new strikers that he is working with, but still thinks that the team has plenty of areas in which to improve.
"We brought a few new players in and had a fresh start in the summer," he said. "Valencia, Sakho and Zarate have all fitted in very quickly and we're off to a flying start, especially after winning on Saturday.
"It is very early days and we're all delighted with where we are at the moment, but we've got a long way to go to improve as well."