Globoesporte says the Ligue 1 side are set to demand £38million for their defensive midfielder in January.
With Thomas Partey and Mohamed Elneny heading to the Africa Cup of Nations in January, and now that Ainsley Maitland-Niles close to securing a move to Serie A giants Roma, Arsenal have prioritised the midfield position in the January market.
"Arsenal approached my agent, but there was no offer. My aim, and I made it clear to Juninho, is to win a title with Lyon," he said.
"The fans have not had one for a long time. We have the Coupe de France, the Europa League and the league. It is difficult with the level that PSG are at, but anything can happen."
However, Guimaraes refused to rule out a move to England in the future.
"My aim is to win a title here, but I have never hidden my desire to play in the Premier League," he added.
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