Nolan struck a late equaliser for the Hammers on Saturday as they salvaged a 1-1 draw against Sunderland.
The 30-year-old played under Allardyce at Bolton and has been one of West Ham's best performers since their return to the top flight which has seen the east London club take eight points from their opening five games.
Sam Allardyce: "No-one should underestimate Nolan.
"Look at his CV. Premier League, Premier League, Premier League - 10 goals, nine goals, 11 goals, nine goals etc. I hope they (other clubs) underestimate him for the rest of the season and he will end up the joint-top scorer like at Newcastle.
"He was great value for money in the Premier League but very expensive in the Championship - so give credit to David Sullivan and David Gold for spending that money on that sort of player."
Kevin Nolan: "I've just got to keep doing what I do, working hard to be in the side, keep scoring goals and being committed,.
"As soon as I stop doing that I won't be in the starting XI."