Grenier's agent, Frederic Guerra, announced on Thursday evening that his client would remain with Lyon, citing the France international's commitment to the club and an apparent belief he was being undervalued.
A further indication that Grenier would not be making a deadline-day move to the Barclays Premier League came when he appeared at Lyon's press conference on Friday morning.
Although Grenier would not rule out a late development, he underlined a desire to remain with Lyon, who stand sixth in Ligue 1 and are targeting a top-three finish.
"I think I will be there. In football everything moves very quickly, but I don't intend to leave. It's not a priority, even if the offers from big clubs make you think," Grenier said in the press conference, according to Lyon's website.
"I'm not someone who leaves like that. Lyon aren't in the right place but we're getting there. I want to stay here to think about my personal goals. The World Cup is one of my objectives."
Saturday February 1
12:45 Newcastle United v Sunderland
12:45 West Ham United v Swansea City
15:00 Cardiff City v Norwich City
15:00 Everton v Aston Villa
15:00 Fulham v Southampton
15:00 Hull City v Tottenham
15:00 Stoke City v Man Utd
Sunday February 2
13:30 West Brom v Liverpool
16:00 Arsenal v Crystal Palace
Monday February 3
20:00 Manchester City v Chelsea
1 Man City 53
2 Arsenal 52
3 Chelsea 50
4 Liverpool 46
5 Tottenham 43
6 Everton 42
7 Man Utd 40
8 Newcastle 37
9 Southampton 32
10 A Villa 27
11 Swansea 24
12 Norwich 24
13 Hull City 23
14 C Palace 23
15 West Brom 22
16 Stoke City 22
17 Sunderland 21
18 West Ham 19
19 Fulham 19
20 Cardiff 18