According to The Telegraph Lampard is one of the candidates being considered for the vacant position at Ibrox following Beales sack on Sunday.
Lampard is believed to be among the list of contenders for the job alongside AZ Alkmaar coach Pascal Jansen and Philippe Clement.
It is believed that the Chelsea legend will need to be convinced of the clubs plans, having managed in difficult situations at both Everton and Stamford Bridge.
Beale was sacked just seven games into the season with the side sitting in third, seven points behind their bitter rivals and league champions Celtic.
Their disappointing start came despite a hefty summer spree by their standards on nine arrivals who, aside from Jack Butland, have failed to impress.
The Ibrox outfit acted swiftly after their 3-1 defeat to Aberdeen and ended Beales 10 month stint at the helm as supporters demanded change.
Lampard could be set for his third job of 2023. He was sacked by Everton in January before taking charge of Chelsea and winning just one of his final 11 games.
Dessers has made six appearances in the league and scored just one goal while Balogun has made just one league appearance.
Copyright 2023 Completesports.com All rights reserved. The information contained in Completesports.com may not be published, broadcast, rewritten, or redistributed without the prior written authority of Completesports.com.