Both Clare and Winn have done well since joining from Mansfield Town and Scunthorpe respectively.
Clare, who hasn't scored yet, will stay at the International Stadium until January 1st on loan, while the club continue to talk to Scunthorpe about Winn, who has scored in two consecutive matches.
If a deal isn't made for Winn then his late equaliser against Brentford could be his last contribution to Gateshead Football Club as his loan deal runs out on Friday.