David Cameron is said to be considering making the job of immigration minister a Cabinet-level position and handing it to current party chairman Grant Shapps.
A senior Conservative Party source told The Huffington Post UK that the move could be made at the next reshuffle, expected at the end of May in the wake of the European parliamentary elections.
The change would allow Downing Street to stress the importance the prime minister places on addressing voters' concerns about immigration.
At present the job of immigration minister sits in the Home Office below home secretary Theresa May and is held by James Brokenshire.
The move would also permit Cameron to appoint a new chairman ahead of the 2015 general election and draw a line under what is likely to be a damaging third place finish for the party behind Labour and Ukip in the European elections.
The appointment could be seen as a demotion for Shapps, who was only made party chairman in September 2012 when he replaced Baroness Warsi.
Since then there have been some grumblings about his performance. The Conservatives slipped to third place behind Ukip in the Eastleigh, South Shields and Wythenshawe and Sale East by-elections. One Tory MP told the Daily Mirror in December that Shapps was a "dead man walking" as Cameron's election strategist Lynton Crosby wanted to ditch him.
Some conservative commentators have also been agitating for a new Tory chairman. The Daily Telegraph's Iain Martin recently said that while Shapps was "enthusiastic", the job should be given to education secretary Michael Gove.
The senior Tory source told HuffPost UK that Conservative business minister and former deputy party chairman Michael Fallon is being lined up for Shapps' job at CCHQ.
It was suggested that the new immigration job would not be a full cabinet minister post but it would allow the holder to attend cabinet meetings - as Baroness Warsi, Ken Clarke and Dominic Grieve do at present.
The two most recent immigration ministers have not had an easy time. Mark Harper, a safe pair of hands who had been tipped for a cabinet job, resigned from the post in February after it was revealed he had employed an illegal immigrant.
Harper's replacement, Brokenshire, put his foot in it with his first speech last week when he attacked the "metropolitan elite" for employing migrant workers. The speech was widely ridiculed given Cameron himself has hired foreign-born nannies to help his family with childcare.Suggest a correction