Tomlin enjoyed a successful loan spell at Ashton Gate last season and has been heavily linked with a permanent move this summer.
Lee Tomlin enjoyed a successful loan spell at Bristol City last season
Having scored six times during an impressive 18-game loan spell at the Championship club, Tomlin has been heavily linked with making a permanent move to Ashton Gate this summer.
Lee Tomlin in action with Sunderland's Younes Kaboul
He tweeted: "I know I've had a lot of messages from the Bristol City fans but no official offer has been made."
Tomlin, who is currently on holiday in Spain, joined Bournemouth for £3 million in the summer of 2015, and is under contract at the Vitality Stadium until 2018.
I know Iv had a lot of messages from the Bristol city fans but no official offer has been made— Lee Tomlin (@Leetomlin10) June 21, 2016
There is clearly still interest from City in signing Tomlin, with boss Lee Johnson keen to strengthen his squad as they bid to improve on last season's disappointing 18th-placed Championship finish last season.
However, talking to BBC Points West, Johnson appeared to suggest that a deal was still some way off.
He said: "I enjoyed working with him and if there is ever an opportunity to bring a player of that quality in, of course we'd be interested.
Bristol City manager Lee Johnson admits he is interested in signing the forward
"He had a fantastic spell. If it becomes possible, we'll certainly be at the front of the queue."
Signing Tomlin would add gloss to an already successful summer for Bristol City, having already snapped up Norwich City midfielder Gary O'Neil and Preston North End midfielder Josh Brownhill.
Johnson has not ruled out further signings, but he admits the club are likely to face intense competition in the transfer market.
A permanent move to Bristol City still seems some way off for Lee Tomlin
"I'd like to have had one or two (more) but we're certainly in the mix for three or four," he added.
"It's just a case of 'can we get them over the line?' But of course there is serious competition, because we're after good players."