In early April, Celtic announced a combination of salary reductions and wage deferrals for the first team, coaching staff, and club executives.
The club posted profits of £24m for the final six months of last year, which they ended with nearly £33m in the bank.
But with the season curtailed and fans not expected into grounds for the start of the new campaign, Premiership clubs have been forced to take action.
Both Hibernian and Aberdeen are in talks with players about wage cuts and, asked if more action could follow at Celtic, Lennon said: “I don’t know. [Chief executive] Peter [Lawwell] and the board will gauge that week by week.
“We’re all on a deferral and cuts until the end of this month, then we’ll probably take a view on that at the end of June.”