Wrexham have signed goalkeeper Danny Ward, forward Ryan Hardie, defender Liberato Cacace, midfielders George Thomason and Lewis O’Brien and forward Josh Windass during the close season.
Parkinson said the club have had dialogue over the idea of signing Denmark midfielder Christian Eriksen, but it “had not gone further”.
The Wrexham boss is still hoping to add to his squad before their Championship opener at Southampton on Saturday, 9 August.
“Obviously in an ideal world you want all your signers in prior to pre-season to work with,” Parkinson told BBC Sport Wales.
“But it just doesn’t work like that. People sometimes say, why doesn’t it?
“It’s just a variety of reasons – clubs don’t want to sell players, competition for players, negotiations over transfer fee or wages.
“Of course, ideally, we’d like to make a couple more additions. Is that going to happen before the start of the season? It’s difficult to say.
“But the most important thing is by the end of August we’ve got a squad in here which we feel can compete.”