The former Ipswich and West Brom boss has signed striker Marc-Antoine Fortune from Nancy for a reported fee of £3.8 million while also recruiting midfielder Landry N'Guemo on a season-long loan deal from the French club.
However, Grant, a former Celtic midfielder, insists the search for players continues.
"We know we have a hell of a lot of good quality players here," the former Celtic midfielder told Sky Sports ahead of Wednesday's friendly against Cardiff in Wales.
"If we can bring others to make the squad better and stronger, and get the guys up to the level that they are capable of, then hopefully we will have a very good side and one that is capable of progressing weekly and hopefully progressing in the Champions League
