The 34-year-old required surgery following his loss via a unanimous points decision at Wembley’s SSE Arena on November 18.
Gutknecht fell ill in his changing room after the fight and was subsequently taken to hospital with the British Boxing Board of Control confirming his is in a “stable condition”.
Groves, who retained his WBA International super-middleweight title on the night, has set up a fund to help the boxer and his family.
He took to social media on Wednesday to provide an update and urge the public to donate to the crowdfunding page.
Groves Tweeted: “Out of respect for Eduard and his family’s privacy I haven’t Tweeted anything about his medical situation so far.
“However, he is still in hospital in a coma after having surgery the night of our fight 12 days ago.
“Thank you to my friends and family who have already donated, it’s much appreciated.”
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.