Keane, a versatile 19-year-old defender, has appeared twice for Sir Alex Ferguson's first team in this season's Capital One Cup.
Both players are eligible to face Bolton in the Championship on Tuesday night, meaning attacking midfielder Lingard is set for his league debut ahead of his 20th birthday next month.
"We have been operating with a smaller, more balanced squad this season, but we felt the time was right to increase the options available to us," said manager Nigel Pearson on Leicester's official website.
"Not only do Michael and Jesse add a great deal of quality to the group, they are also the type of hungry, young players that will fit in well with what is already a very strong squad."
Heading into the Reebok Stadium clash, Leicester sit fourth in the Championship table.