"We have got a project to complete and the gaffer has stated before that whatever happens in the summer, will happen in the summer," Deeney told talkSPORT.
"It is very flattering (the Arsenal interest). My son is an Arsenal fan so he read it in the paper the other day and I do not think he is happy that I am staying at Watford."
Deeney has found the net six times in the league this season, and has formed a formidable partnership with Odion Ighalo up front, scoring a combined 20 league goals in as many games.
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Their exploits have lifted Watford to ninth in the Premier League, four points off fifth place Manchester United and a possible European spot.
Ighalo, too, has drawn reported interests from bigger clubs but Deeney insisted the Nigerian was staying put at Vicarage Road till the end of the season.
"He is not going to leave in January. The manager and the owner have made that clear," Deeney added.
"The pleasing thing from my point of view and from Iggy's (Ighalo) is people want us. That shows that we have been doing something right for the past five, six months."
Watford host Newcastle in the FA Cup third round on Saturday, before travelling to the south coast four days later to face 13th placed Southampton in the league.
(Reporting by Nayan Das in Bengaluru; editing by Amlan Chakraborty)
