Gutierrez was left out for last weekend's defeat to Tottenham and revealed to a fellow Twitter user that his absence was not due to an injury.
On Thursday, Carver confirmed he had been involved in a disagreement with the Argentine, who had previously hinted at frustration on social media.
"There was a situation on the training ground, which happens. We have shaken hands like men," Carver said.
"We had a conversation and moved on like grown men."
Newcastle face Swansea City on Saturday looking to end a run of six straight defeats amid a backdrop of fan protests and fears of relegation to the Championship.
"We need a win. It's so important for everyone and may just lift that bit of gloom that's over the city at the moment," added Carver.
Siem de Jong, meanwhile, is in line for his first Premier League appearance since August.
De Jong has endured dreadful luck with injuries since joining Newcastle from Eredivisie side Ajax in July, playing in just three games.
The Netherlands international was sidelined until January with a groin problem and then saw his initial attempt at a comeback thwarted by a collapsed lung - an issue he also suffered with while at Ajax in 2013.
However, Carver said: "Siem de Jong will be in the squad and be involved. Some of his play in the Under-21s at Aston Villa was excellent."
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