The offence happened at around 8.20am on the North Sea Lane area of Humberston on Wednesday
A man on crutches approached the girl and attempted to push her towards a small white van.
She was able to get away and was left" shaken but unharmed", officers said.
Detective Inspector James Fairgrieve said: “We’re really grateful to everyone who has been in touch so far with information. We have a number of lines of inquiry that we’re following up.
“However, we now have more up to date information about the van involved.
"Initially, it was said to be a Transit-style van, but we now understand it to be a smaller compact van, similar to those often used by builders and other trades.
“If you have seen a man of this description or a small white van in the area, please get in touch on 101, quoting crime reference number 16/34589/18.
“You can also call Crimestoppers anonymously, on 0800 55511.”
The culprit is described as being thin, around 5ft 9ins tall and in his 50s.
He wore a black beanie hat, a black zip-up fleece and black tracksuit bottoms with white stripes on the legs.