The 23-year-old striker joined the Cumbrians last month on an initial one-month deal and impressed, netting two goals in six appearances.
Abbott told the club's official website: "Mike has proved an excellent addition to the dressing room and squad since he arrived. He brings something different and we think there's still more to come from him."
Grella will remain with the club for another two months but could be recalled by the Whites at 24 hours` notice, after they inserted a clause in the deal.