The two Premier League big hitters are leading the race for the England Under-20 defender, who has also attracted interest from Tottenham and Newcastle United.
Arsenal stepped up its pursuit of Lascelles by dispatching chief scout Steve Rowley to watch him in action against Bolton Wanderers last Saturday.
Forest is braced for offers this month for the highly rated center back, who has been compared in some quarters to a young Sol Campbell.
The Championship club does not want to lose Lascelles but accept that it would be difficult to reject a bid that matches their 3-million-pound valuation.
One of the conditions it will place on a sale in this window is that the 20-year-old spends the rest of the campaign on loan, much as Wilfried Zaha did when he joined Manchester United from Crystal Palace a year ago.
Forest’s terms could put off Arsene Wenger, who refused to agree to loan-back deals when Arsenal was negotiating to sign Theo Walcott and Alex Oxlade-Chamberlain in the January windows of 2006 and 2011. Oxlade-Chamberlain eventually moved from Southampton the following summer.
Tottenham came close to signing Lascelles in the summer of 2012 after he had been recommended by David Pleat, the former White Hart Lane manager and director of football, who had been advising the club in an unofficial capacity on young English players since leaving his role as a consultant to Forest the previous year.
The 6ft 2in defender, who is regarded as one of the best central defenders in his age group in the country and has been capped at Under-18, Under-19 and Under-20 level for England, has established himself in the Forest team during recent months and the club is reportedly hoping to offer him an improved contract.