Alexander was put on leave earlier in the week

But assistant manager Gary Simpson will be leaving the Red Imps as part of a mutual agreement.

In a statement issued on Thursday, chairman Steff Wright apologised for the "unfortunate sequence of events" which led to Alexander's suspension.

"We are pleased to announce Keith will be remaining with Lincoln as per his existing contract," said his statement.

"We would like to confirm that any issues were totally and completely resolved and this will allow Keith to resume his duties without any compromise or actions on our part.

"At this point the board would like to apologise for the unfortunate sequence of events leading to his suspension and this act had nothing to do with anything he was responsible for."

Alexander and Simpson were put "on leave" after meeting with the board at Sincil Bank.

Youth coach John Schofield took charge of the team for the goalless draw against Mansfield Town on Monday.

Lincoln, who have not won for four games, lie 15th in League Two.