The 19-year-old arrived at Cappielow with countrymen Tomas Peciar and Michal Habai last month and played in a friendly against Sheffield United.
Kamenca, however, was forced off at half-time after aggravating a hamstring injury, and a potential contract offer was put on hold.
But that move appears to have been rekindled, with Morton boss Allan Moore confirming that Kamenca is expected in the country next week.
Moore told the Tele: "It looks like young Tomas is coming back over next week.
"He's still got a few things to get sorted in Slovakia but we have agreed to bring him back over.
"I still think we need another striking option up there.
"We've only got two at the moment and young David [McNeil], who came on and scored a good goal on Saturday.
"Tomas is only 19 years of age, physical, has a good touch and I think he has something to offer.
"We've set aside a space in the budget so we're hoping we can get something done and dusted."
Meanwhile, Morton players will sport squad numbers on the back of their shirts in the upcoming league campaign, the Tele can confirm.
Starting with tomorrow's opener against Cowdenbeath, they will be as follows:
1. Derek Gaston, 2. Scott Taggart, 3. Marc Fitzpatrick, 4. Tomas Peciar, 5. Jonathan Page, 6. Mark McLaughlin, 7. Joe McKee, 8. Dougie Imrie, 9. Tony Wallace, 10. Archie Campbell, 11. David O'Brien, 14. Reece Hands, 18. Michal Habai, 21. Fouad Bachirou, 22. Thomas O'Ware, 23. Nicolas Caraux, 26. Aidan Fulton, 27. David McNeil, 28. Glenn Eadie, 29. David Verlaque, 30. Luke Irvine, 31. Nicky Jamieson, 32. Aidan Ferris, 33. Cameron O'Neil, 34. Craig Knight, 35. Mark Russell, 36. Jordan Cairnie, 37. Steven Lamont, 48. Kabba-Modou Cham.