Forwards Calvin Zola, Clayton Donaldson and Anthony Elding all arrived at Gresty Road last summer but have failed to make an impact, netting just 12 goals between them.
But with funds running low after relegation to League Two, Thordarson cannot bring in any replacements and has backed his existing players to improve their goalscoring prowess
He told the club's official website: "I would love to get a proven goalscorer in, who could score 20-plus goals a season but they are expensive. They cost money and last season this Football Club spent a lot of money on players to do that.
"I have strikers in house who have done reasonably well but have not delivered goals on a regular basis. So a striker is not a priority for us, but I will be looking.
"We have a lot of strikers here and they need to deliver. Whoever comes into the team and bangs goals in then they will get the shirt. It is up to them to prove that they are worth a place in the side."