The 29-year-old, who is out of contract this summer, held talks with manager Gary Holt yesterday but is no closer to signing a new deal after a hugely impressive campaign in the second tier.
"The talks will keep going and hopefully they come to a conclusion sooner rather than later," McGovern said.
"I love it at Falkirk and I am playing regularly.
"But I am ambitious and I want to play at as high a level as I can. It's a difficult one, but I do enjoy life at Falkirk."