'nonreimbursable' is formed from the prefix 'non-' (from Latin 'non' meaning 'not') plus 'reimbursable' (reimburse + '-able'). 'Reimburse' ultimately traces to Middle English 'reimbursen' and Old French 'rembourser', with the root related to Latin 'bursa' meaning 'purse'.

'reimburse' changed from Middle English 'reimbursen' (influenced by Old French 'rembourser'/'embourser'), which in turn derives from roots related to Latin 'bursa' ('purse'); 'reimbursable' was formed by adding the adjective suffix '-able' to 'reimburse', and 'nonreimbursable' is the modern negated form using the prefix 'non-'.

Initially the root sense was 'to put back into a purse' (i.e., restore money), which developed into 'to repay or compensate'; 'nonreimbursable' has the modern meaning 'not eligible for repayment/compensation'.