Mr Khan asked Transport Minister Andrew Stephenson about the possibility of a Denby Dale bypass in parliament.
Mr Khan said: "Interconnectivity is vital to the prosperity of our northern towns and cities. In order to ensure Wakefield is better connected to neighbouring communities and is more accessible improving road capacity and routes is needed.
"Can my right honourable friend outline whether a bypass between Wakefield and Kirklees will be considered in the third road investment strategy to better connect us with Huddersfield, Manchester and beyond while easing pressure on the M1 and M62 around Leeds and Bradford?"
Mr Stephenson said it was a matter for Kirklees Council, which would be able to bid for money from the government's £4.6bn "levelling up" fund.
A similar matter was raised in 2019 when Flockton residents asked for a bypass to reduce traffic in the village.
At the time Wakefield Council’s portfolio holder for transport, Matthew Morley, said a bypass would result in more congestion in the village of West Bretton, which lies three miles to the east of Flockton.
Coun Morley said: “The impact on West Bretton would be devastating because Junction 38 of the M1 would be a much more desirable route. “We cannot support this. It wouldn’t be fair to Kirklees, it wouldn’t be fair to West Bretton and it wouldn’t be fair to the long-term aspirations ofthe Wakefield district.
But within minutes of that, Kirklees Council put out their own statement, which was at odds with Wakefield's position.
Kirklees statement said: “We un derstand local residents’ desire for aFlockton bypass which is why we have looked at a scheme
several times over recent years.
“We are looking to carry out a study into the benefits of up- grading the A637 which may also includeabypass for Flock ton and other improvements in the area.
“However, this study would come at a significant financial cost. We have been unsuccess-ful in putting the scheme for- ward for inclusion in bids for funding up to now but we will continue to pursue this.”
Wakefield Council has been approached for comment.