The 22-year-old Englishman will start training with the Buddies on Friday.
Lennon said: "I became aware of Dom through an agent. Kansas City's season is over and there are one or two of the MLS players trying to get over (to Britain).
"It has been on the back burner for a month to six weeks but Dom is over now.
"It would only be a short term one for us so we will have to wait and see but the reports we have had on him are positive."